I always thought of it like this. Obi Wan is basically meant to be in exile, he’s known as a hermit by Luke, so most people probably don’t even know he exists on the planet.
The reason Luke knows? Because his uncle told him and knows himself why Obi Wan is in exile. That’s two people that know him as Kenobi. The few other people he comes into contact with knew him as Old Ben, because that’s who he told him he was, he likely never gave them a last name. So when Luke hears about him, he’s Old Ben the hermit. When he asks his uncle about him, his uncle simply fills in the last name.
It’s not really a concern that Luke knows it, and it’s pretty unlikely for him to bring up Ben, even less for him to use the last name in conversation.