Funny how this thread came up just now - I actually watched Dumbo on the Disney channel just a couple hours ago!! Was doing some channel surfing, and there it was. No one else was home so I parked myself on the couch and watched it the whole way through!!
I'm trying to think of when they actually use the name Timothy, but all I can think of is at the very end with all the newspaper headlines. They mention his name in the last headline as Timothy Q Mouse.