Yes, he is referred to as "The Vision" several times in the movie.
Initially, you're correct that the word wasn't used as a name, it was used to describe Stark's "vision" of a new AI. Ultron also later refers to the android as "my Vision."
However, the Avengers do use the word in such a way that it's clear they've decided that his name is "The Vision". For example, Tony refers to him by name during the climactic battle:
Stark: FRIDAY! The Vision?
FRIDAY: Boss, it's working. He's burning Ultron out of the 'net, he won't escape through there.
Also, in the final scene, Thor decides to leave
The Mind Stone
with the android:
Thor: If he can wield the hammer, he can keep [spoiler]. It's safe with the Vision. And these days, safe is in short supply.