I agree with Peter. This is an interesting question and one that many brands face. It reminds me a little of a similar question that was asked recently here in Q&A regarding ampersands in brand names.
Here's my advice. Part of writing your business plan should include determining certain "branding" rules and guidelines. These should include official logos, colors, fonts, style sheets, etc. Make all of that play into your branding. Then, stick to it like glue unless there's some earth-shattering, mind-warping reason to rock boat and change it.
Like Peter, our brand name is two words "CCI Solutions." Our brand name is further complicated by the fact that there are probably a dozen or so other "CCI Solutions" in the world, spanning industries from HR, to healthcare to online learning. We've suffered difficulty giving our brand an "identity" because of our own inconsistencies and ambivalence towards what we call ourselves and how we present ourselves. If your presentation is inconsistent, your potential loyal fans are going to be confused and confusion is something you never want when carving out a place for yourself.
Choose one or the other using careful consideration and common sense, and then relentlessly stick to it and drive it home.