I suppose if people were going to name their kids after time of the year, maybe not months, but themes could work.
Here are some that came to mind:
Valentine,
Valentin,
Valentina and other variations for babies born close the
Valentine's day.
I suppose floral or botanical names could work for spring.
Daisy,
Violet,
Florian,
Lily, etc.
Pascal and
Pascale also works for spring, since it refers to the latin form for
Easter.
There are also season names themselves:
Summer and Autum.
Just my two cents. :)
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