Flower

Blossom and Bloom

In English, not many people are called Flower or Blossom, but it is more common in other languages.

Probably the best known flower name is the French, Fleur.
It comes from the Latin word, florentius which means 'blossoming' – there are varieties of it too:

Fleur
FLEUR: French form of Roman Latin Flora, meaning "flower."
FLEURETTE: Diminutive form of Fleur meaning "little flower."
FLORETTE: English variant spelling of French Fleurette
FLO: Short form of Florence and Flora
FLOELLA: Modern English compound name composed of Flo "blossoming/flower" and Ella "foreign; the other."
FLÓRA: Hungarian form of Latin Flora, meaning "flower."
FLORA: Roman Latin name meaning "flower."
In mythology, this is the name of a goddess of flowers and spring.
Pet names are Florine, Florrie, Flossie and Flo.

Interestingly, the name FLORENCE and it's varieties is often given to boys as well as girls.

FIORE is used in Italy by both boys and girls.
FIORELLA: Feminine diminutive form meaning "little flower." Fiorello is the masculine form.

FIORENZO: Italian form
FIORENZA: Feminine form of Fiorenzo

FLORENTINO: Italian form (masculine)
FLORENTIA: Feminine form

FLORIAN: Short form
FLORIANA: Feminine form

FLORIANO: Italian form
FLORINE: Pet form of Roman Latin Flora

And in other languages...
FIRENZE: Hungarian form of English/French Florence
FLORENCE: English and French feminine form
FLORENCIO: Portuguese and Spanish form
FLORENCIO: Portuguese and Spanish
FLORENTIN: French form
FLORENZ: German form
FLORENTIY (Флорентий): Russian form
FLORENTXI: Basque feminine form
FLORICA: Romani name perhaps derived from the Romanian word Floarea, meaning "flower."
FLORIN: Romanian form
FLORIS: Dutch form
FLOWER: English name derived from the vocabulary word, "flower," from Proto-Indo-European *bhlo-, meaning "to blossom, flourish."

Bláth

BLÁTHNAT in Irish Gaelic means "little flower."
In mythology, this is the name of a maiden who loved Cúchulainn, the hero of Ulster.
Bláth is used as a girl's name.
Bláithín (little flower) is also liked
Blaanid (a form popular in Manx)  are also common.

In Cornish there's Blejan

And in Welsh (the Welsh word for flower is blawd)
BLODEUEDD: derived from the word blawd, meaning "flowers."
BLODWEN: meaning "white flower."

Other names in other languages which simply mean flower are:

AMISI: Egyptian name meaning "flower."
ANFISA (Анфи́са): Russian form of Greek Anthousa, meaning "flower."
ANFISA (Анфи́са): Russian form of Greek Anthousa
ANTHEIA (Άνθεια): Greek name meaning "flower."
In mythology, this is the name of a goddess of flowers, gardens, love, marshes, and swamps. She was worshiped on Crete.
ANTHOUSA (Ανθούσα): Greek name

BLANCHEFLEUR:  is a variant spelling of French Blancheflour, meaning "white flower."
BLUMA (בְּלוּמָא): Yiddish name meaning "flower."
BOPHA: Cambodian Khmer name meaning "flower."
BUPPHA: Thai name meaning "flower."
BUSSABA: Thai name meaning "flower."

CALANTHE: Variant spelling of English Calantha, meaning "beautiful flower." This is the name of a genus of orchid flowers.
CHUN-HUA (1-春花, 2-春华): Chinese name meaning "spring flower" or "spring magnificence."
FIORALBA: Italian name composed of the elements fiore "flower" and alba "dawn," meaning "flower of dawn."

GHONCHEH: Persian name meaning "flower bud."
GONCA: Turkish form of Persian Ghoncheh, meaning "flower bud."
HANA (花): Japanese name meaning "favorite" or "flower."
HARÉRÉ: Egyptian name meaning "flower."
HOA (pron. hwa): Vietnamese name meaning "flower."

KAMI: Short form of Chamoru Kamia, meaning "flower."
KAMIA: Chamoru name meaning "flower."
KUKKA: Finnish name
KVETA: Czech name
KOSUM: Thai name meaning "flower."
KUKKA: Finnish name meaning "flower."
KVETA: Czech name derived from the word kvet, meaning "flower blossom."

LEILANI: Hawaiian name meaning "heavenly flowers."
LORE: A Basque name used by both boys and girls
LULE: Albanian name meaning "flower."
LULJETA: Albanian name composed of the elements lule "flower" and jete "live," hence "flower of life."
LULUDJA: Possibly a Romani form of Albanian Luljeta, meaning "flower of life."
LULEZIM: Albanian name meaning "blooming; flowering."

MALEE: Thai name
MANSI: Native American Hopi name
MELANTHA: English name thought to probably be an elaborated form of the Greek word anthos, meaning "flower."
MISAKI (美咲): Japanese name
MADOKA (1-円, 2-円花): Japanese name meaning "circle, flower."
MAI'ANA: Chamoru name meaning "flower."
MALEE: Thai name meaning "flower."
MAYLEA: Hawaiian name meaning "wildflower."
MELANTHA: English name thought to probably be an elaborated form of the Greek word anthos, meaning "flower."

PUSHPA (पुष्पा): Hindi name meaning "flower."
QUETZALXOCHITL: Nahuatl name meaning "precious flower; queen."

RAYEN: Native American Mapuche name meaning "flower."

SETHUNYA: African Tswana name
SIHU: Native American Hopi name meaning "flower."
SACNITE: Mayan Nahuatl name meaning "white flower."

TSVETA: Feminine form of Bulgarian Tsvetan
TSVETAN (Цветан): Bulgarian name meaning "flower."

VIRÁG: Hungarian name meaning "flower."
XIUYING (秀英): Chinese name meaning "beautiful/elegant flower" or "surpassing beauty."
XOCHITL: Nahuatl namemeaning "flower."
ZAHRA:  Arabic name
ZAHUR: Egyptian name meaning "flower."

You do have the name Blossom in English, though it's not very common any more. Names meaning 'blossom' are common in many other languages.

ADSILA: a Native American Cherokee name 'blossom'
BLOSSOM: 19th century pet name derived from Old English blōstm, meaning "flowers on a fruit-tree (or ornamental tree)."

BRYONY: English name derived from the flower name.
The name derives from Latin bryonia, from Greek bryo, meaning "to grow, sprout, swell."
BURBUQE: Albanian name meaning "bud; sprout."

CHLORIS: Latin form of Greek Khloris, meaning "green buds."
In mythology, this is the name of a goddess of flowers and vegetation.
CVETKA and CVETKO (Цветко): Slovene name derived from the Slavic word cvet, meaning "blossom."

EFTHALIA (Εφθαλία): Modern spelling of Greek Euthalia, meaning "blooming, flourishing."

GHONCHEH: Persian name meaning "flower bud."
GONCA: Turkish form of Persian Ghoncheh, meaning "flower bud."

GWRI: Welsh myth name of Teyrnon's adopted son, "Gwri of the golden hair," who grew to full adulthood in seven years, meaning "bloom."

IZDIHAR (إزدهار): Arabic name meaning "blossoming."
KIELE: Hawaiian name meaning "fragrant blossom; gardenia."
KVETA: Czech name derived from the word kvet, meaning "flower blossom."
LULEZIM: Albanian name meaning "blooming; flowering."
MISAKI (美咲): Japanese name meaning "beauty bloom."
MUKUL (মুকুল): Hindi name meaning "blossom, bud."
NITZA (נִצָה): Hebrew name meaning "flower bud."
NOURA (نورة): Arabic name meaning "blossom."
NOORA (نورة): Variant spelling of Noura, meaning "blossom."
NAWRA (نورة): Variant spelling of Noura, meaning "blossom."

POLOLENA: Hawaiian  meaning "blossoming."
SAKI (咲): Japanese name meaning "blossom."
SAKIKO (咲子): Japanese name meaning "blossoming child; earlier child."
SEMADAR (סְמָדַר): Hebrew name meaning "bud" or "blossom."
SETHUNYA: African Tswana name meaning "bloom, flower."
THALES (Θαλής): Greek name meaning "blossom."
THALEIA (Θάλεια): Greek name derived from the word thallein, meaning "blooming, flourishing." In mythology, this is the name of the muse of comedy and pastoral poetry.
YAMKA: Native American Hopi name meaning "blossom."

Many varieties of the Arabic word for blossom exist:

ZAHIR (ظهير): Arabic name meaning "shining; blossoming."
ZAHIRA (ظهيرة): Feminine form of Zahir
ZAHRA:Egyptian name meaning "flower."
A Variant spelling of Arabic Zahrah, meaning "blooming flower."
ZAHRAH (زهرة): Arabic name meaning "blooming flower."
ZAIRA: Perhaps a variant spelling of Arabic Zahrah, meaning "blooming flower."
ZARA (زهرة): Variant spelling of Arabic Zahrah, meaning "blooming flower."

ZAINAB (زينب): Variant spelling of Arabic Zaynab, derived from the name of a "flowering plant."
ZAYNAB (زينب): Arabic name derived from the name of a "flowering plant."

Posy
Can't forget this lovely name...
POSEY: Variant spelling of English Posy, meaning both "bouquet, flower" and "(God) shall add (another son)."
POSIE: Variant spelling of English Posy, meaning both "bouquet, flower" and "(God) shall add (another son)."
POSY: English name derived from the flower name which originally meant "a line of verse engraved on the inner surface of a ring," but later acquired the meaning "bouquet, flower." Compare with another form of Posy.

And finally...

MANSI: Native American Hopi name meaning "plucked flower."

NOXOCHICOZTLI: Female Nahuatl name meaning "my necklace of flowers."

POLIKWAPTIWA: Native American Hopi name meaning "butterfly sitting on a flower."
POSALA: Native American Miwok name meaning "farewell to spring flowers."
POURASDAN: Armenian name meaning "flower garden."

SHABNAM (শবনম): Hindi name derived from a Persian word meaning "dew drops on flowers."

VARTAN: Armenian name meaning "giver of roses."
XOCHIPEPE: Nahuatl name meaning "flower-gatherer."
XOCHIPILLI: Aztec myth name of a god of love, music, and flowers, meaning "flower prince."
XOCHIYOTL: Nahuatl name meaning "heart of a gentle flower."
YOLOXOCHITL: An alternative spelling