I insist the frog be called "Donald"
... because I insist that one use the subjunctive whenever appropriate, otherwise it will die out ;-)
To avoid misunderstandings, I would like to state that what follows is not addressed to anyone in particular.
Of course, we can use what I will call here the "naked" subjunctive "be" if we wish. However, it seems a little overly formal for a conversation between a father and his daughter (see the OP for context), so I chose the more informal "should be" as a widely accepted, and in my view correct, alternative. That's the context argument (obviously influenced by my assumptions about the daughter's age, etc., which may or may not be appropriate).
Now I come to the audience argument. My post was addressed to the author of the OP, and I therefore made certain assumptions about him. His profile contains no information regarding the level of his English. The sentences offered in his original post do not suggest advanced level to me, so I thought it appropriate to keep my answer as simple as possible, which to me meant not exploring the usages of the subjunctive mood in a single LEO post. That should not stop any other user giving it a shot, though. ;-)