Three's A Crowd.
You have lots of good suggestions to choose from. I especially like "Cover Two" and "The Coveralls" (and if you go with this one, wearing coveralls as your stage attire would be a great gimmick). Is there something in your two names (whether given names or surnames) that can be exploited for purposes of a band name? For example, back some years ago two friends of mine formed a duo. They never came up with a specific duo name, and the duo was relatively short lived (maybe that was partly the reason why?). They weren't related, but both of their last names are Brown. I suggested to them several times that they use "Los Dos Browns" (Spanish, or rather "Tex-Mex" for "The Two Browns").
Well... I thought about our initials. My buddys initials are HJ and mine are AC, so I figured HJAC could be pronounced as "Hey Jack", or something... similar to GP =Jeep. Far fetched perhaps. And cheesy. Not that there's anything wrong with cheese.