In general, the term for dislocation is luxation, and a partial
dislocation is subluxation.
Since you specifically asked about the elbow, there are two
bones that could have been dislocated from the humerus, the radius
and the ulna. Ulnar luxation is pretty rare, but radial subluxation
is actually pretty common, and is easy to fix.
So the term you are probably looking for is radial head
subluxation.