Do you think Tramp is an "appropriate" name for a dog?

No not really. Its even ben used for kids movie titles. "Lady and the Tramp". But if you use it in a bad way then it is. I don't know how but all i know is that some T-shirts have something bad on them for the word "Tramp". + Tramp is also kinda of a another word for mutt expect for male mutts only.