Three agents have held the number 34 over the years:
Max makes contact with Agent 34 #1.
1. Dour-faced CONTROL agent who specialises in secreting himself in confined spaces - a prototype for the similarly talented Agent 44 and Agent 13. Seen stationed in an airport locker in New York [Episode #1: "Mr. Big"] and in a restaurant food trolley [Episode #4: "Our Man in Toyland"].
Max with Agent 34 #2.
2. An Agent 34 is seen working part-time as a cab driver during the 1967 CONTROL budget cutback. It seems unlikely given his much brighter demeanor that this is intended to be the same man so the number must have been reassigned at some point.
The second Agent 34 is portrayed by Ralph Leabow [Episode #65: "Maxwell Smart, Private Eye"].
PITS Agent 34.
3. Unusually strong and attractive PITS agent stationed in Austria. She guides Max to Edith Von Secondberg's chalet in the mountains.
This Agent 34 is portrayed by Sylvia Kristel [Movie: "The Nude Bomb"].