Stanford, like Harvard, Princeton and Yale, are large research universities with worldwide reputations. Pomona, like Amherst, Williams and other top LACs will always "suffer" in the name recognition battle against the bigger schools. If that kind of name recognition is very important to you, then maybe Pomona (or any of the LACs) may not be your best match.
My son is a Pomona sophomore. People often confuse Cal Poly Pomona with Pomona College, even here in California. It doesn't bother him at all. He realizes that not everyone is a college prestige junkie! Also, he has seen the reactions of people when they hear where his sister went for her undergrad, and he's glad he doesn't have to deal with that kind of pressure, or deal with some of the negative stereotypes that go along with a more famous college.
And when people HAVE heard of it, the reactions are always extremely positive. "Oh wow, that's a great school! " is the usual reaction. That's IF they have heard of it.
I will add this. When you get to Pomona, you will be amazed at the calibur of students in your class. Any of them would have managed just fine at the big name universities.