I second this. (Can't use CVerse examples because I'm not very familiar with it) Scott Hall is in WWE's HoF as Razor Ramon, not as Scott Hall, but any database where he's in the HoF, he has to be in there as Scott Hall.
That's not too big of a deal as his WCW run and 2002 WWE run were under his real name, but if I try to induct The Dudley Boyz, Edge & Christian, Brutus Beefcake, countless others, I have to hope they're under the right name or go in and change it, which messes with other things.
If the Dudleys are in both the WWE and IMPACT Halls, then they're using the wrong names for one of them since they weren't allowed to use the Dudley name in IMPACT, so they're either in IMPACT's HoF as The Dudley Boyz, or WWE's HoF as Team 3D.