What should we call ourselves when we share decision-making power?

First, let me congratulate you for coming up with a governance model that will horrify most “good governance” commentators but that sounds like it works.  A 17-year business partnership like yours can create a stability that is rarely matched by nonprofits with rotating boards and changing executive leadership.

I am familiar with one Pennsylvania nonprofit corporation that was run for more than 25 years by two women founders who called themselves Co-Directors.  When the organization was founded, they put their husbands on the board of directors with them. But when the Pennsylvania nonprofit corporation law was changed to permit a board of fewer than three directors, the husbands were asked to resign.  The women became the only ones on the governing body. 

The women had complimentary skills, but similar values.  They could hold “board meetings” virtually any time they wanted merely by walking to the next office.  They operated on the philosophy that when decisions had to be made, they would talk through the issues and, somewhat like a Quaker consensus, if either one of them was strongly opposed to an idea, they wouldn’t do it.  They maintained an “advisory board” to help consider strategic proposals and to involve a wider swath of the community in their program.  But they were the chief executives and the only actual decision-makers.  It was a relatively small organization, but very successful at what it did.

It isn’t clear from your question whether your model is actually similar. But they found that the title of Co-Director worked well for them and communicated their joint decision-making authority.  It might also work for you.