And Aragorn and King Theoden were roughly the same age. It’s mentioned in the appendices that when they were both youths getting some combat experience, they fought together under King Thengel as allies of Gondor in some of the many battles they had against Mordor. Theoden didn’t recognize him because he traveled under a fake name back then, and it wouldn’t have occured to Theoden that this random dude (as far he knew) that looked half his age could possibly be his old battle comrade.