What is a person who speaks on the mic that which person is going to come next to speak called?
1 short for master of ceremonies.
2 a person who provides entertainment at a club or party by instructing the DJ and performing rap music.
Master of Ceremonies noun
a person who presides over a formal event or entertainment and who introduces guests, speakers, or entertainers:
the Master of Ceremonies will announce the cake-cutting
There is also the word compere.
a person who introduces the performers or contestants in a variety show.
If this person is directing speeches in a political context, they may be the chair (-woman or -man or -person) or (esp in British use) the speaker. In an academic setting, they may be the moderator.
MC (Master of Ceremonies) is a common word for that. However, sometimes (especially in certain specfic contexts and settings) that person might simply be called a "host".
A master of ceremonies is the host of a staged event, whose duties include the presentation of speakers or performers. The term is not specific to British English. It's frequently abbreviated “MC” or “emcee” (and often applied metaphorically to rappers in hip-hop music).