Examples include Amherst, Auburn, Boston, Bryn Mawr, Clemson, Columbia, Davidson, Georgetown, Ithaca, Oberlin, Princeton, the Savannah College of Art and Design, Swarthmore, Syracuse, Temple, Wellesley and Villanova.
In addition to including the name of the city in which the institutions are located, the following include “university” in their names: Akron, Albany, Buffalo, Baltimore, Charleston, Chicago, Cincinnati, Dallas, Hartford, Houston, Indianapolis, Mobile, Phoenix, Pittsburgh, San Diego, Scranton, St. Augustine, Tulsa, Urbana and Utica.
Neither of my lists contains all of the schools named for the cities in which they are located. However, having the city’s name and/or “university” associated with that city’s name has done little to limit the focus, reputation or enrollment of each institution.
Therefore, it is neither provincial nor shortsighted to consider naming the combined universities in Augusta “University of Augusta” or retaining the current name of Augusta State University.