I'm with Karkarov. I also like that by taking two classes you become something specific, not just two classes but something that can be recognised by the world. Grim Dawn does this, and I enjoy looking up the different combinations to see what they make. Plus, if you enable renaming, then it'll be harder for them to implement responses to what you are ingame since you might rename a combination to something vastly different in concept. No, I love the combination names and I hate the idea of renaming them.
First, I am against renaming classes in general whether base classes or combinations- seems a bit silly, but no big skin of my notice if it is possible.
Second, I'm not sure the world can see the difference between a Paladin 20 and and a Paladin 19/Fighter 1. Insofar as it is possible for anybody in the world to recognize such characters by their deeds, one is clearly a Paladin... and so is the other.
If we assume it makes sense for the world to recognize a person by class in the first place, it makes absolutely no sense to me that the world would start to recognize a character as something different merely by the smallest of changes.
Which is why I am against composite class names in the first place, unless they are allocated more restrictively for people where one class doesn't clearly dominate. As an example, one could choose as a rule than none of the classes be at least twice as high level as the other, which would come to:
A player with class A is known to the world as class A.
A player with classes A and B is known as class A if A >= 2*B, and as class B if B >= 2*A
A player with classes A and B is known as composite class C if none of the above apply, i.e. A < 2*B and B < 2*A.
Example, total class 10
10, 9/1, 8/2, 7/3 are known as A
6/4, 5/5, 4/6 are known as C
3/7, 2/8,/1/9 are known as B
Example, total class 20
20, 19/1, 18/2, 17/3, 16/4, 15/5, 14/6 are known as A
13/7, 12/8, 11/9, 10/10, 9/11, 8/12, 7/13 are known as C
6/14, 5/15, 4/16, 3/17, 2/18, 1/19 are known as B
That said, I'm not sure it makes sense for the world to recognize the player by class rather than deeds, looks, or renown in the first place in the vast majority of cases, but it does seem to be the convention.