Should I mention a professor's name in my SOP for MSc if the professor is only taking PhDs?
There is no reason you shouldn't mention the professor's name and your interest in his field. It will show that you are focused. 

In the US, the master's degree is often (usually?) seen as a step along the way to a doctorate, so you will probably be perceived that way in any application. Also, a Master's in the US will usually not be entirely research focused and will include quite a lot of course work. You will be able to meet with him if you are accepted and can work toward some relationship with him. If you think you aren't quite prepared to work under him as a PhD student, the work toward the Master's degree should get you closer to that goal. You might also find that your goals change, of course. 

Since he is a new professor he isn't likely to be tenured. This can be a problem for students as he will be very focused on his own research and work towards tenure. This means that he may have less time for students. He may also have an agreement with the university that he can focus for now on his research with (only) advanced students. 

But treat work with him and his group as a tentative thing. But stating that you have an interest in that can do you no harm and may serve you well.