Isn't this too order-dependent? What happens if you add code prior to another usage? For instance, I start out with:

if (Person.blah) {
    doSomething();
}

I'd want to also get completion for if I added a use of Person.blah before the if statement:

Person.blah/**/

if (Person.blah) {
    doSomething();
}

If you have multiple uses, the value in the table becomes -1 and no filtering occurs

Ah, okay. I misunderstood.

Why don't you use an enum that would make this explicit?

const name = (node as Identifier).text;
nameTable[name] = hasProperty(nameTable, name) ? NameTableState.Once : NameTableState.Many;

or at the very least, leave a nice big comment explaining what you're doing here and what -1 means.

Because we need the position in the case where it's Once.

Ah, right. You're not checking the current identifier and asking "should I actually show this", you're just grabbing up identifiers. I'm not sure why I missed that.