+1
I don't think it should be a required thing, but the ultimate solution is to make it an option. So that everyone who wants their name on, can, and everyone who doesn't, can have the option not to.
I really don't see the negative in making anonymity an option at all.
Maybe if a code was placed at the end of the tag. (Ex: Anonymous Trainer#99237) Each tag is assigned to a player, so if their toxic and pm you while in a PVP match, and they have the anonymous mode on, it would show that tag, so you can still report and stuff. Just an idea that covers all viable points, but could probably be done better.
I also think rivalry, and making the ladder more interesting isn't a really viable point IMO.