Calling a section of Ulster by the name of the whole province isn't a casual matter of words having different definitions. "Ulster" used in this sense is sectarian. It has been used as a way of falsely implying that there are is a longstanding historical basis for the partition of Ireland, going back centuries.

I wasn't in any way suggesting that Pied Piper was using it for that reason. But think the use of the term in this way is better avoided. "Northern Ireland" is a neutral and generally accepted term for the territory involved (even though it's not strictly accurate geographically).

As for Hong Kong - as I understand it the lease was for New Territories, what you might call Greater Hong Kong. Hong Kong itself is much smaller, and that wasn't on lease.

Guantanamo seems a funny sort of lease - it can only be terminated if the US Government as well as the Cuban Government requests it, according to a treaty of 1934. Which essentially means it was annexed - except that pretending it hasn't been annexed gives the US Government a legal loophole for doing things there that would be illegal if it had been formally annexed.