Reputation
Name Recognition
FHSU appears to be an unremarkable (in either a good or bad sense) state university from a smaller state. It's not a flagship school or particularly well-known for anything. As such, the name recognition of this (or any other equivalent) school will drop rapidly the further away you get from it. In other words, it will be most well-known in the area where the school is located, and least well-known at the other end of the country or of the world. People in a far away state will be very unlikely to have heard the name of this school. Wisely they have kept the "state university" in their name, which helps people anywhere in the United States form an instant estimation of the level of education that you may have received. FHSU should look no different in your resume than just about any of hundreds of other state universities around the counrty.
Impact of Name Recognition
To reinforce this idea, judging by countless discussions I have read on this topic, the general consensus online appears to be that unless you graduate from one of the top (5, 10, or 20 at most) CS schools in the country, the name of the school has very little bearing on whether you are considered for a position or not. CS curriculums are fairly standardized, and regional accreditation (see below) ensures that you received a quality of education that meets at least some minimum thresholds. This means that since your degree will come from an accredited state university and most people will not be familiar with 99% of state universities in the country, they just will not be able to tell the difference between your school and most other applicants' schools.
School Accreditation
FHSU is accredited by one of the major regional accreditation organizations, like any other legitimate university. This ensures that the university meets or surpasses some minimum standards that would affect the quality of education you receive.
Program Accreditation
This program is not currently accredited by ABET (Accreditation Board for Engineering and Technology). This accreditation is usually a requirement for certain defense industry and government jobs, certain graduate programs, or if you decide to become a patent lawyer after graduating from computer science and then from law school after that. Typical software developer jobs very rarely if ever require ABET accreditation for BSCS degrees, but if you are aiming for one of those specific outcomes, you should look for an ABET accredited program, which, you should know, will require some extra math, natural science, and CS classes. ABET accreditation has specific curriculum requirements that would make it impossible to offer a streamlined program such as this one.