The title of the person who conducts the marriage will depend on which religion he/she/the couple are (or non-religious of course).
In a civil ceremony, the officiant is sometimes a "justice of the peace".
The ceremony in the US can also be performed by a justice of the peace, a judge or any other civil official licensed to perform a marriage ceremony.bishop, vicar, priest, deacon, minister, pastor, reverend . . .
Yes, it depends upon the denomination.
For sure it will be a "church official" who will perform the ceremony.
In the wedding ceremonies in which I have officiated, we have used 'celebrant'.At a humanist wedding, it's a "celebrant" although I have heard the phrase "humanist minister" used once at a funeral.