Are we a data processor or controller?

My company rents out office space and meeting rooms to other organisations. So those organisation are our customers with whom we have a contractual relationship. As part of the office space rental, the staff at the organisations can book meeting rooms. This means that we process the name, contact email and organisation name so that we know who is renting office space, who to bill, and who can book meeting rooms. In this situation, are we a controller or a processor? Should we be signing a data processing addendum?