
when I think in English, it doesn't seem stupid at all, there are actually people named Summer but when I think in my mother tongue I get your point perfectly, no sane Turkish parent would name their kid "yaz". I don't think the author can be blamed for this though, there's really no way to check for this accept asking someone who is a native speaker of the language

It both just sounds very bad and is prohobited. Like, there's an entire list of things you legally can't do when naming your child, and it includes using made-up names (Leto isn't a name in Czech, so it counts as made up), names that could make others make fun of you (e.g. names that sound vulgar or indecent), etc. You can't even name your child "Ivanka" like you could do in the US, because it's actually a short nickname in Czech and not an actual name.

I answered question about names in Czech republic in different topic so I'm just copying my answer:
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 parents 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 and 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. :-*

Actually my mother's name is Ivana and I remembered situation when our neighbor called her Ivanka and she got really mad. She was literally screaming "Do I look like five year-old to you!?" It was hilarious - for us, not for our neighbor. :-D And Ivanka Trump is probably known around the world so she is good example. ;-)
Leto sounds hilarious xDDD No parent would name their child like that.