In boxes with connections in them are junction boxes. And junction boxes must remain ACCESIBLE without dissasembly the building material.

Bascially that means that you can get to the connections with nothing other than a screwdriver.

You can install a blank coverplate and paint it when you paint the beadboard so it will almost disapear. But you want to acutally paint it separate. Otherwise if you every remove it the paint will crack and you see it.

If this happens to be end of run then you can go to the previous box that feeds this one and disconnect the wire. Then you can cover the box as it is no longer in use.

Or you can run a new cable through the basement/crawlspace or attic to bypass the receptacle that you want to abandond.

But remember that code requires any wall space that is bigger than 2ft long must have a receptacel within 6 ft. (Basically a receptacle every 12ft). That even at that it is scimpy number.

I guess I'll probably just leave the outlet. I am putting a new outlet only 2 feet away: the new one is under a new built-in desk, whereas the old one is outside the desk. Thanks.