Full Idea
An expression is not counted as a name unless it succeeds in referring to an object, i.e. unless there really is an object to which it refers.
Gist of Idea
An expression is only a name if it succeeds in referring to a real object
Source
David Bostock (Intermediate Logic [1997], 3.1)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.71
A Reaction
His 'i.e.' makes the existence condition sound sufficient, but in ordinary language you don't succeed in referring to 'that man over there' just because he exists. In modal contexts we presumably refer to hypothetical objects (pace Lewis).