I was leaning toward something simple and alliterative like Deck Dual or Card Commander, but Paul suggested having a backstory that inspires the name. I argued that 1) I'm no good at making up such things, 2) I usually find them cheesy, and 3) that could be a subtitle to the regular, generic name.
Then last night I was letting my mind drift on the topic. I envisioned an arena with thin, angular projections pointing up to form a partial sphere over the combat area. I still had no name and kept thinking No Name, No Name, and Nemo ("no name"), which morphed into Nemyne as the place name.
At first then Nemyne Arena was the name I chose. Later I started writing up the little spiel and for some reason I can't recall, the word 'archon' was stuck in my head. I googled its meaning (it being associated with the 80s computer game in my memory) and found it is a Greek word for leader. Thus I settled on the name Archon Arena, where the lords of Nemyne fight fierce battles for supremacy.
It's short, alliterative, has a back story, and leaves room for expansions. After a few days, I think it fits. What do you think?