PR: my son just went through all this; I would suggest you take a look at the Army ROTC web site. When you apply for AROTC,, you do need to list schools, and the scholarship you get will be tied to one or more of those schools. If it ends up being tied to a school you subsequently do not want to enroll in, or to which you are not accepted, you can ask that the scholarship be transferred to a school that has an open slot. However, with the desireability of these scholarships, as you can see from reading these threads there are many with scholarships but no open slots to the schools they want to go to.
I am not inclined to believe that the Army considers your merit for a scholarship based upon the "name" of the school. I have no inside knowledge on this, but would believe the Army would love to have graduates from top schools enter their service; I can tell you that son recieved AROTC scholarship to three schools, one low cost, one middle of the pack (approx. $25000) and one at about $36000. Note too, that alot of schools include room and board, making the AROTC (and other ROTC) scholarships virtually a free ride (except for the committment!!!!!!)
The other posters are correct, that AFROTC scholarships are not tied to any schools, so long as the school has the major to which the scholarship is tied, as many are. Some AFROTC scholarships are not tied to any particular major, and those litterally can be used at any school. Their downside is that they do not generally pay as much--the type 2 and type 7 have maximum limits on them.
Didn't mean to carry on. Good luck as you learn about the scholarships. They can be a good deal, and there is lots to learn on these forums. Son would have used his AFROTC scholarship but for appointment to USAFA. Good luck.