Most people don't associate the letter F with fashionable baby names, because most F names are fashionable precisely because they're UNfashionable. Names such as Florence and Frances, Floyd and Franklin have geek-chic style that appeals to parents searching for an offbeat name for their daughter or son.
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Along with Florence and Franklin, other cool baby names that start with F in the US Top 1000 include Felicity, Finnegan, Flora, Fisher, Frida, Ford, Faye, and Fletcher. Undiscovered F names that are popular internationally include Fraser, Faustine, Floris, and Fiadh. 
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F is a fun, quirky initial with many cool options ranging from familiar to obscure. Some of the <a href="https://nameberry.com/baby-name-lists/category/cool-names">cool baby names</a> beginning with F include those here.

Cool Baby Names That Start With F

A twee German name likely originating as a diminutive of the word frau, meaning "lady, woman, wife".

Frauke

Fania would make an interesting choice for a child of Irish Russian heritage, being a Celtic name with a Russian Tania-like feel. 

Fania

Cool baby names for boys and girls that start with the letter F, including Franklin, Fisher, Flora, and Fable (Page 6)

Cool Baby Names That Start With F

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