Pardon the short response, but in a few words - yes and no. The Partitio terrarum imperii Romaniae, also referred to as Pariitio regni Graeci, from 1204 shows that both terms were used. It is safe to say that after the Schism the Catholic world began to refer to them as Greek. The Eastern Christians as well as the Muslims continued to mostly call them Roman. As far as I am aware, many Greeks and Turks even until today refer to them as Romans and it certainly a name used in the southern Slavic countries - "ромеи" ( Рωμαίοι , Romans)

I've answered a similar question in the past, which might be helpful here:

What did the other people's of Europe call the Byzantine Empire? Did it differ depending on who you asked and were there any changes as the empire dwindled?