Coming up with a name is tough. My crew went through several differnt ones before coming up with The Elmwood Puppets.
Elmwood is the town where I grew up. I had used the name of the town in a few scripts as a fictional town some of the characters live in. One day when we found out another puppet company had a very similar name to the one we were using I blurted out "Elmwood Productions" as an option, and it all went from there.
I would suggest staying away from a name like the Muppet, or Fraggles for you family of characters. A company name, even something like The Nick-A-Nap Puppets, might be cool!
Good luck!