The phrase "to become a surrogate" means to take on the role or responsibility of another person, especially in regards to caring for their child. Full definition
What are the rules and recommended guidelines for becoming a surrogate mother? (pregnancymagazine.com)
They end up at a motel where the manager (Meat Loaf) who basically becomes a surrogate for the audience. (seligfilmnews.com)
After your initial decision and meetings with your agency, part of becoming a surrogate involves undergoing the psychological evaluation. (surrogateparenting.com)