So far, two classes have a canon full name in the franchise, those being Engineer, aka Dell Conagher, and Demoman, aka Tavish Degroot. Others only have canon last names, with two possible exceptions. I also discovered that the Blu Scout had been named in the comic by the Blu Soldier as "Judas", as seen in "The War on Smissmas" comic. So far, this is a collection of names that I have found.
Scout: (First name: possibly Judas) Soldier: (First name: Possibly Jane) Doe Pyro: Unknown Demoman: Tavish Degroot Heavy: (First name:Misha (short for Mikhail))Recently confirmed in the more recent comics Engineer: Dell Conagher Medic: (First name: possibly Fritz) Sniper: (First name: possibly Rick) Mundy Spy: Unknown
If anyone can find more info on possible names, please leave a post!