Wilds and Wildes both feel really, really weird and awkward to me. But even though Wilder is in the category of names that usually isn't my style at all, I do kind of like it - I think because of Laura Ingalls Wilder. My opinion would change if it were the middle name, though, and it would become "Why did they make Wilder his middle name if that's what they intended to call him?"
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https://www.behindthename.com/pnl/120652