Well... in Sun and Moon, I received a male Eevee nicknamed "old granny," all in lowercase letters. I don't know if I kept him but his weird nickname makes me laugh to this day, and I can't remember any other as funny as that one.
I gotta say though, the circumstances under which I got a Mimikyu over Sw/Sh Surprise Trade were funny and heartwarming too. After a few failed trades, I closed my eyes, and wished with all my heart to get a Mimikyu to breed so I could go on with my playthrough. When I opened my eyes, there she was - a Japanese Mimikyu! She went on to sire not just Merlin, the Mimi that accompanied me on my first Shield run, but also Mikel, the one that tagged along for my second run. They are now all reunited in my second save file. What an adorable and powerful bloodline they are.