I will try to answer your inquiry, although I admit I am not very into the Varna clubs' affairs
I don't think Spartak fans call themselves 'hooligans', some of them call themselves 'fanatics' who actually are the hard-core fans getting into fights, I have the unfortune to know one of these guys
, and even these fans are into fractions like “Mladost Boys ‘ 95 “,Vladislavovo Fans”, Arise Gays, Chaika Supporters, Patriarha Boys и Zone Nish
I'v heard that soona new click will appear :' Bad Blue Boys'
Spartak varna players are called 'sokoli'(hawks) an dsome fans identigy themselves with that name as well. When Spartak was established they were in a very bad financial state because the club was established bu two young players in the poorest meighborhood of Varna
While, Cherno More is the older club(1913 while Spartak-1918) and the richer, in the beginning of its history it is called Ticha.
hope this clarifies it
Basically your information is correct