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First there is no tradition of using seasons (or other common nouns) in names. Only two names that I can think of are based on Spring (Jaro) and that is Jaroslav (translation is something like Celebration of Spring) and Jaromír (simply Spring + Peace). I don't know about any other names based on Summer, Autumn or Winter (Léto, Podzim, Zima in czech).
Secondly parent in Czech republic cannot name their child in every way they want to because of laws of child protection. The rules are simple: The name have to exist in some calendar at the world (sometimes are recognized names of characters in books, TV series or movies); the name must be grammatically correct; the name cannot be shorter, longer or be composite of two or more names, it cannot be garbled, diminutive or homely (cute versions of names). If the name that parents select is very unusual they need an expert opinion - they pay for it to special office, the charge is 600-1100 Kč (around 26-48 USD so no big deal) and sometimes happens that the name is unauthorized and parents have to choose different one. Good example of how name should an shouldn't look like by czech law is Ivana and Ivanka Trump - Ivana is correct version however Ivanka is diminutive and not allowed. If Ivanka was born in CZ and not in USA she couldn't be named that way, she would have to have the same name as her mother Ivana. (Ivanka is version of name that you can call little child or someone really close to you like partner, sibling or best friend because it's infantile).
There is no list of allowed names (because in the world is too many names) but there is list of unauthorized names - I did'n check it but I think that name Léto is not allowed (or it will be problematic to authorize Léto as a name) simply because it's not a name but noun.
I hope I answered sufficiently comprehensive. :-*
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Hihihi.. To jo přímo REVOLUCE... (⌒▽⌒)... Já jsem si četla... Jedu automaticky... A najednou mi to cvakne... Léto... Tak se vracím a čtu to znova... No jo je to tam ...
Když jsme u těch českých slov... Četl jste někdo tu mangu o husitech? Začíná to ošklivě... Znásilněnim... Atd... (︶︿︶)
Upřímně zvládla jsem jen pár kapitol...
Léto. Wow. As a person from Czech republic I can tall you that Léto is weird name and no parent will probably never use it. But as a fangirl I have to say it´s great. ヾ(❀╹◡╹)ノ~