How are Orthodox monastic names chosen? Orthodox monks seem to always acquire monastic names when they join a monastery. Thus Mikhail became Macarius. (They also acquire a "seminary surname" if they did not have one already, though this seems not to happen any more since the newcomers already all have surnames.)

What rules or process guide the selection of the monastic names? Are they supposed to be Greek? Who makes the decision as to a name and what is it supposed to represent?
The monastic name is given at the Small Schema tonsuring by the person that performs it (a bishop or an abbot). It is him that chooses this name. He may or may not consult the monk himself or his community about it.

The names don't have to be Greek. But they should be the names of existing saints or ones that relate to some Truths of Faith.

The name is meant to honor a particular Saint and to endow the monk with a holy patron and a figure to imitate.