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You can call yourself whatever you want. There's much more to DC than just the "important" comics DC tells you are important.
People who've never read a comic from before 2000 that wasn't either Justice League or event related are no more DC fans than someone who has only read series too obscure to even be fully collected now.
I think all that's really required to be considered a fan is that you like something enough to actually want to be called a fan of it.