I want to have a button under "IM Names" so the user can change the field label to what they want, IE Yahoo, MSN and so on. Any advice on how to make this button perform this action?

Why not just use a Value List?

That would work if I needed to name the fields, but to change the "Label" of the field...won't work.

You should use another field called type. You can use a merge field as the button itself or you can still use your button.

Either or, you should change the value of this other field and to the users it can look like a field label. If you want, you can have your users choose it as a popup menu with a value list as Lee pointed out.