I am currently writing my statement of purpose (SOP) for top graduate schools in engineering majors in US. I am wondering should I include name of my potential advisor on my SOP (Is it a good idea to do that)? The problem is I am thinking if I do not include name of advisor it might be the sign I did not look at his/her research page and I am not very specific about my plan. On the other side, if I include name of potential advisor and my application is not competitive or he/she is not accepting any graduate student this might cause others not to look at my application since they might think I am not interested in their research.
Faculty at a top-10 school in aerospace engineering gave a former student of mine the advice of indicating several professors whose research he was interested in, for exactly the reasons you suggest: by showing too narrow a scope, it makes it harder for other researchers to gain interest, and by just submitting a "generic" SOP, you run the risk of looking like you're not doing your homework. Showing an interest in several faculty makes it easier for someone to advocate for you in the admissions committee.
I think it's standard to list some potential advisors. It shows you know what you want and you have a good reason to be interested in the school. And if none of the advisors you want are taking students, do you really want to attend the school in the first place?
(In the long run I think it's better to get rejected from a school than to go there and realize there's no one there who wants to work with you who you would also be willing to work with.)
I would also go into some detail about the area of research you are interested in. This is a good chance to display your familiarity with the topic/maturity as a researcher, and it will help them assess whether they have spots for you.