The reason Voldemort brainwashed Bellatrix was in order to marry her in absolute secrecy, unconventionally taking her last name for his own (this is also the reason she is not married to Lestrange in MoR). As a result, his name will show up as “Tom Black” on the map, and Dumbledore’s “Find Tom Riddle” instruction will do nothing.
The Founders may have been Truenamers, in which case each person who walked in would have a singular name attached to them.
So the Map can’t find married women?
The reason Voldemort brainwashed Bellatrix was in order to marry her in absolute secrecy, unconventionally taking her last name for his own (this is also the reason she is not married to Lestrange in MoR). As a result, his name will show up as “Tom Black” on the map, and Dumbledore’s “Find Tom Riddle” instruction will do nothing.