It could be, but they recombined the two high schools (Taft and Garfield) in the early 80s. Might be for some older citizens.Is that the reason, or is it to differentiate Hamilton HS from the era of when Hamilton had 2 public HSs?
I hear Hamilton High or HHS colloquially, too.
Taft's building is now Hamilton High School (although it has undergone extensive renovation and expansion.
Garfield has been a middle school for decades.