Has had

It means that two years ago, he stopped shaving.

AlpheccaStarshe stopped shaving.

I see. In other words, he has experienced wearing a beard for two years.

Anonymoushe has experienced wearing a beard for two years.

That's what usually happens when a guy doesn't shave for two years.

AnonymousHe has had a beard for two years. Does "has had" mean 'has displayed' or 'possessed' in the sentence above?

All three expressions mean the same thing, even if it's a fake beard in a box! However, "possessed" is more likely to suggest a fake beard in a box than the other two. Another synonym which is very common goes like this:
.
He has

Thank you, CJ, for the reply.