It's not possible to find the trainer's name through Advance Map, but: you should have a script program 'linked' to A-Map, like "XSE" by HackMew. Anyway, if you double-click the trainer in A-Map, their script should open in XSE, and if you look through the text that appears you should find a line that says something like 'trainerbattle 0x0 0x72 0x0...'. You see that '0x72'? That's the Trainer's ID. If you search the numbers after the 'x' in A-Trainer (in this case, you would search '72'), then you should find the Trainer you're looking for :)