I have a psychology degree, and have been working as a programmer in the mainstream video game industry for the last thirteen years.
For me, having the psychology degree (rather than a computer science degree) was a major hurdle to getting hired as a programmer, and if I had it to do over again, I'd almost definitely get the computer science degree instead of the psychology one.
But you're not talking about getting hired as a programmer; you're talking about a job in design. And specifically which degree you get is less important for design jobs than it is for programming jobs, so I think you wouldn't have any trouble at all justifying why you wanted the psychology degree.
In fact, I think one could make a very strong argument for why psychology would be an ideal degree for a game designer. Alternate strong contenders might be history, literature, philosophy, filmmaking, and similar broad disciplines which cross across a lot of areas of knowledge. As a game designer, you really want a wide breadth of knowledge, rather than a lot of depth in a single area. Check Tom Sloper's site for more details about further useful areas of study.
I will mention, though, that I've personally found that working in the game industry can be doubly stressful when you have a background in psychology. I've trained rats in skinner boxes, and I've been through the process of vetting human studies for ethics violations. And sometimes, the things you get asked to do to your players start feeling more like the players are rats in skinner boxes, rather than humans in ethically designed tests. And that can be a bit distressing, sometimes.
Or at least, that's been my experience. None of my colleagues have ever seemed to notice or be bothered. And so I assume that it's just my psychology background which has made me hyper-sensitive to this sort of thing. So I thought I'd mention it.