In Muslim communities Christians have always been called as "Nasrani" (at least in where I'm living). Lately we have been hearing it in the media since ISIS has been persecuting Christians there. Allegedly it is an Arabic transliteration of Nazarene (from Jesus of Nazareth). Is it true? If it's true, why it was the word "Nazarene" that got transliterated to Arabic instead of "Christian"? Did any Christians, maybe early Christians, ever addressed themselves as a Nazarene?
Well the derivation is accurate.
It's helpful to first remember that 'Christian' is a term that originates in Greek and is then brought over to Latin, and only gets promulgated in the European/Mediterranean context. Jews contemporaenous with the early church in the 1st and 2nd century would not call Jewish-background believers 'Christians', or any equivalent term, i.e. 'Messiah-ists', probably because it legitimates their claim that Jesus is the Messiah.
Instead, the evidence suggests that in Aramaic, and likely other semitic languages, the term used is 'Nazarene', i.e. followers of the guy from Nazarith.
Tertullian and Jerome both mention the term 'Nazarene', and appear to understand it as an adjective referring to Christians.
Later on, by the 4th century, you can see one evidence of this in reference to 'Nazarenes' as a Christian sect of Jewish heritage in Greek writings, i.e. Epiphanius of Salamis' Panarion](http://nazarenespace.com/page/panarion-29-the-nazarenes)'.
Notzrim survived into Rabbinic Hebrew as a term for Christians, while nasara and nasrani appear in the Qu'ran. It's thus very likely that the term was a widespread and common usage to designate 'Christians' in semitic languages.