Higashi no Eden, Phantom: Requiem for the Phantom Recommendations
The protagonists get their memories wiped clean and the organizations that did it uses them by getting the protagonists to work for the organization. In both stories the characters are given false identities. They begin shady dealings for the organization while they set out to discover more about the secrets of the organization and their own true identities.
Both are about a Japanese teenage male who wakes up in America with his memories wiped, and then them dealing with situations that arrive, but Phantom is more of an espionage/action thriller, while Eden is a bit tamer and doesn't have so much death.
Both series center around a talented young Japanese man forced into a web of intrigue and high stakes crime in the USA (Higashi no Eden begins in Washington DC, but most of the action is in Japan). Each main character has memory problems and a female ally, and seemingly no way to escape the secret organizations they've been recruited into. Requiem for the Phantom is a lot heavier, with more violence and less comedic relief, but both are full of suspense and are well drawn. I even enjoyed the dubbed versions of both, which is extremely rare for me.
They both revolve around an amnesiac trying to uncover their past.
Both main characters have to live the lives they are now faced with, with no knowledge of their past life.