Q:

When did "The Batman" become "Batman"?

In Batman's first appearance in Detective Comics No. 27, he is referred to as "The Bat(-)Man" exclusively.

In the issue, characters say "It's the Bat-Man" rather than "It's Batman".  For example:

It's the Bat-Man — get him!

In which issue does a character refer to him as just "Batman" for the first time? In particular, when is "It's Batman" (with no definite article) used for the first time?
For the purpose of this question, hyphenation ("Bat-Man" vs. "Batman") is unimportant.

A:

Interestingly, there are actually three four answers to this question...
The Narrator
The first time that Batman is consistently referred to as "Batman" (as opposed to "The Batman") by the omniscient narrator is Detective Comics #95, some 7 years after his original debut. 

In-universe characters
Batman is inconsistently referred toas "Batman" (no 'the') by both the narrator and quite regularly by various in-universe characters from Detective Comics #33 onwards, only 12 issues (2 years) after his debut:

His Logo
Batman lost his "the" from the Title logo in Detective Comics #114 in 1946, 9 years after his original debut:

"It's Batman"
The first instance I could find of that specific phrase being uttered is in Detective Comics #110, in which Batman (and Robin) assist Scotland Yard with their inquiries:

