It seems with each of our kids we've had a song that we sing to/about them, though it's not necessarily related to their name.
Patrick we sang a little tune we created, "small man, small man, he does the things he can." Sorry, no video!
Eli we sang the theme from "the good, the bad and the ugly" with his nickname, Boo, so it went "Boo-ee-oooo-ee-oooo.... wah wah waaaaaah...."
Caroline we sang plenty of "Sweet Caroline," of course, but we MOSTLY sang "Little sister"
With Ethan I've taken to singing "Small One," from an old Disney/Don Bluth short film. I don't know how I picked it (actually, I'm not sure how most of our nicknames and songs come about, they just do!) but it sure seemed to fit, and it's nice to remind myself that even though he's growing at an atrociously fast pace he still is my small one :)