Taskmaster isn't a particularly well known public figure, and he likes it that way. Those with criminal connections would likely know of a man who calls himself the Taskmaster who does mercenary jobs if the paycheck is right. He's also known to be a maddening opponent for law enforcement and "low-level" supers due to some yet unknown ability.
Those who have connections with SHIELD, AIM, and/or HYDRA, however, know a great deal more. Taskmaster is a mercenary, of course, but does most of his work training various henchmen/agents for those organizations, as well as for other various governments and paramilitary groups. He's rated a high class threat by SHIELD, as he has been able to best a significant portion of their agents with little effort.
For those in the know, Taskmaster is currently employed by the Xavier Institute as an extracurricular physical education teacher who is working, oddly enough, without pay. No one quite knows for sure why, but it appears that after a meeting with Xavier himself, Taskmaster chose to lend his talents to the school for educational purposes.