I was just contacted by the sister of a friend in California, who informed me that her brother, whom I had been friends with between 1998 and 2002, when I was living in California, had passed away and left some inheritance for me. However, he left it to me in the name he knew me by, which is a religious name which I was ordained with and have gone by since 1979, but I never made it my legal name. Does that disqualify me from receiving the inheritance he left for me?

No but you would need to prove that you are the same person mentioned in the Will.