In the TV show "Quincy, M.E." what was Quincy’s first name?

It was never mentioned.

R.

Quincy's first name was never verbally mentioned during the entire Quincy, M.E. TV show run. The only clue to what it was appeared in Episode #33, "Accomplice To Murder", where his business card is seen with his name written as "Doctor R. Quincy". Jack Klugman says that the question he's most often asked by fans is, "What is Quincy's first name?". He answers, "Doctor!".
https://en.wikipedia.org/wiki/Quincy,_M.E.

The absence of a given name for Dr. Quincy served no obvious purpose other than as a gimmick. (The other characters referred to him as "Dr. Quincy" or simply "Quincy"; their lack of curiosity about his other name might be partially attributable to the fact that Quincy can be used as either a first name or a surname.) The only clue the audience was ever provided about Quincy's first name occurred (in the episode "Accomplice to Murder") when he handed a battered housewife his business card — sharp-eyed viewers noted the card identified him as "R. Quincy". Those who tuned in for Quincy's final-season wedding to Dr. Emily Hanover expecting his full name to be revealed were disappointed (just as viewers were at Agent 99's wedding to Maxwell Smart) — they heard only: "Do you, Quincy, take this woman . . ."

http://www.snopes.com/radiotv/tv/nonames.asp