I could see them merging with Cap's old Stars and Stripes network into a new Liberty Legion...sort of an informal support network like the Buckaroo Banzai Blue Blaze Irregulars. But not calling themselves Captain America.
Sam's problem with being Cap is the same one John Walker had. He brought his personal belief of what Cap should be and should be doing dictate what he did as Cap. John was too far right and Sam was too far left.