The term pagan has always been pejorative and was introduced when Christianity became state religion. It included all non-christian religions. During the Middle Ages even Mohammedans were called pagans or heathens, although their religion was built on Christianity.
During the late Empire, when the need arose to distinguish between Christians and non-Christians, Emperor Julian used the term "Hellenist". This seems to be a more proper and neutral name for what the Christians call "pagans".
Of course a follower of Isis would call himself "Aegyptian", a follower of Marduk would call himself "Babylonian". A certain nationality implied a particular religion. The idea of following a different religion, independent from nationality, was a new phenomenon introduced by the rise of the mystery cults in Rome and of course Christianity, which was essentially just another mystery cult.
If somebody calls himself by the pejorative term "pagan", he tacitly acknowledges Christianity, because without the antonym "Christian" the term makes no sense. He should better call himself "Hellenist" as Emperor Julian did, or whatever pantheon he adheres.