The general public doesn’t know Penn and Penn State are two different universities. Many think of Temple and Villanova as Philadelphia’s main universities, and have never heard of Haverford or Bryn Mawr. In short, the general public is not a good measure of universities.
La Salle has a good “brand” in the Philadelphia area, including crossing state lines. It’s got quite a few catholic/parochial feeder schools in the area. Not a national powerhouse, not a “Mainline” school, and not an intellectual school, but definitely respected; especially well-known among Catholics, for nursing, social work, and education, and for its strong core curriculum requiring theology and philosophy from all graduates; they are considered well-educated and reliable.