Learn English – Is “got insane” a correct sentence with a meaning

It means that it was after 2 pm - so there weren't many people around (they'd finished their lunches earlier). It is not particularly good English - rather colloquial.

Clearly, you could substitute almost any time and end up with an equivalent expression. You could have some other expressions such as "it was gone AWOL" (I went looking for the TV remote but it was gone AWOL - absent without leave).

You should not assume that either refers to a Company (which is a legal structure) since either term could also be used for a partnership or another corporate structure.

You are correct in inferring that using Boston Consulting tends to focus attention on the entity as a whole and their shared capabilities while Boston Consultants emphasises the individuals that make up the group and their particular expertise.

The choice is probably more concerned with "branding" or image than with governance. There is no reason that one man operating out of his garage could not register and use the name Boston Consulting to disguise the fact that he is the only consultant available (and perhaps the receptionist as well.)