All "conventional mages" are illusionists.The only magic they can perform is trickery, to make people think they have magic. Ambient magic is the only kind of magic that can actually do anything.
Tris will be the only one of the four kids to take a mage last name in the usual way.Most mages replace their family names with last names that reflect their powers or just sound cool- e.g., Niklaren Goldeye, Yarrun Firetamer, Aymery Glassfire, Olennika Potcracker, etc. The four main characters haven't done this so far. It's stated that Briar isn't going to- he chose "Briar Moss" and he's going to keep it. Sandry and Daja both have reasons to keep their full names- Sandry is very proud of her noble birth and her family, Daja is equally proud of her heritage. Tris has more or less disowned her family, so it wouldn't be that strange if she took a new mage name eventually. Also, her book will be about her going to Lightsbridge- the academic mages' university- and she might take a mage name after that, to reflect having learned academic magic.