Is there an official name for the many-to-many relationship table in a database schema?

I call it a cross-reference table.

Some may not consider this an official term, but it's certainly a popular one. I mean, you'll find plenty of relevant results in Google if you search for it. The other thing I like is that it can be easily abbreviated "xref" and then used in your table naming scheme, e.g. "table1_xref_table2". That'll get everyone on your team calling it the same thing.

UPDATE:

Wikipedia calls it a junction table. It's strange that I've never heard that term but I suppose different circles call it different things. As we're finding out -- there is no single official answer.

The most common name is "Join Table" in my opinion, but I have heard several others you have listed. So, I would say "no", there is no "official" name :-)

This is HIGHLY unscientific, but I thought it would be interesting to see how many Google results were associated with the combination of common answers to this question and the term "many to many".

Based on this, it looks like "join table" is the most commonly used term for the...um...joining table in a many-to-many relationship.

The combined search terms

"join table" "many to many"

return around 13,700 results in Google.

"link table" "many to many"

returns around 4,700.

"junction table" "many to many"

returns around 3,500.

"association table" "many to many"

returns around 3,300.

"relationship table" "many to many"

returns around 3,200.

"intersection table" "many to many"

returns around 1,500.

"cross-reference table" "many to many"

brings back 1,000.

gerund "many to many"

only returns 450.