Yes that's what it refers to, originally Red Rose Rock FM when Red Rose split frequencies. Wikipedia says that it was originally going to be based in Blackpool but that plan fell through
I don't think it has any connection with it serving Blackpool, it would have been a rather tenuous link. I think it's more to do with the fact in the past rock was often used as a synonym for pop, and Red Rose Rock sounded quite a snappy name.
By the 1980s, certainly in the UK, the word “rock” was very much associated with electric guitar bands and the hard rock and heavy metal genre. You wouldn’t have referred to the majority of Rock FM’s playlist as “rock music”. That said, their jingles “Rockin’ the North West... Rock FM” suggested a more generic/traditional interpretation of the word - music you can “rock” to.
Incidentally, most of the music kids listen to these days makes me rock - back and forwards in a corner with fingers in my ears.
Cut out the coupon in your TV Times!