It depends what you're talking about here. Some person you might bump into at a bar occasionally, and don't ever keep up with, then no. A person you've known for an extended period of time in your life, but haven't seen in years, then yeah, you should remember them.
I can remember most everyone I went to school with from like the 3rd grade and on, for instance. If I was shown a class picture from those years, I'd get 90% of them. Most of the people I've ever worked with too. I don't think that makes my memory special.
However, in Biden's case, it goes far beyond forgetting people's names. The guy can't remember when he was Vice President. Two terms...in one of the most prominent positions on the planet...can't remember when he held that job. That's a bit more concerning than flubbing a name here and there. That's why he looks bad, and not because he simply appears old. That Carville dude looks like fucking Hans Moleman, but he doesn't appear to have lost any wits, or an ability to keep up with a conversation.