Naturally on a first meeting with teh Dashwoods, Will would say he was staying at Allenham... however I presume he knew Eliza in Bath for soem short time before he took her away and he met her, in company with her freind and possilby other people. So I would imagine that in hte course of conversation, he might say where he came from. Or during the course of his relationship wiht her, they must have talked occasionally.