Generally: -
Flight Deck operator
PIC - Person in Charge
Tug operator
Taxi Endorsement
Aircraft Marshaller
All of the above are company approvals that any LAME/AME can and do hold. There are a number of pre-requisites for each.
Taxi movements must have minimum x 2 approved LAMEs on the flight deck.
Tow approvals must utilize 1 of each of the above. No taxi endorsement required. PIC runs the whole show. Marhalling as required.
No requirement for flight crew for any engine runs unless you need a seat filled.