Mister Buddwing (1966)

A well-dressed man wakes up on a bench in New York's Central Park, with no idea of who he is, or how he got there. All he can find in his pockets are a train schedule, a couple of drug capsules, and a piece of paper with a phone number on it. On his right hand: a ring with a cracked stone; engraved on the inside of the band is the inscription, "From G.V." Armed with these meager clues, the man, adopting the name "Buddwing" (inspired by a passing Budweiser beer truck and a plane flying overhead), sets out to learn his true identity. Along the way, he encounters a variety of people, including three different women who each reminds him in some way of someone named "Grace."