Where does 别间 ("other") as in 别间大学 come from?
It's not a standard term, but it's understandable.  I don't know if it's a dialect.  It's not common in any areas I have lived in.
I'd understand it as its literal meaning:
别: other
间 is a measure word for room (房间).
You can compare its usage to 这间, so as a demonstrative. E.g. 这间酒店.  I suppose you could say 别间酒店. Basically, it should have something to do with &quot;house or room&quot;.
Some might frown at the term.  However, I think it could be a good name for a hotel, restaurant, etc.  E. g. 别间酒店, 别间饭店. Compare to 有间客栈(which appears in a book I've read before).