You must select programs wisely, keeping in mind that “fit” is the critical factor. That is to say, if you wish to focus on Kantian epistemology, then be sure to apply ONLY to departments with at least one Kant scholar and at least one specialist in epistemology.

I also advise you to make sure you have documented reading ability in either French or German before you apply to any graduate programs. Most programs these days are extremely competitive, and applicants with no research languages often do not make the cut.

It might also be wise to apply to one or two “terminal Masters” programs. These usually serve as “feeders” to PhD programs, so great work at (and great recommendations from faculty in) these programs will enhance your applications a great deal.

Finally, and most directly in answer to your question, your undergraduate program’s reputation can enhance, but will not usually damage, your applications. Superb letters from your professors, a terrific writing sample, and a literate and focused statement of purpose that shows facility with method and theory in your subfield are the factors that will make or break your application.

I wish you every success.