After looking at the other guy's website (such as it is) I can see why you wouldn't want to risk confusion.
I think a good question is: What are client expectations in the market you want to pursue? Do potential clients want to be dealing with an individual person, or would they feel comfortable dealing with a firm?
If they want to deal with an individual, I think T. A. MacPherson, T. Alex MacPherson, Alex MacPherson, or even Alexander MacPherson would sound fine and would differentiate you from the other guy. Timothy Alexander sounds rather dignified, too.
If they don't have problems dealing with a firm, you've got a world of possibilities such as MacPherson Studio, MacPherson Imaging, MacPherson Associates (surely you associate with somebody) or some clever combination such as Alexander & MacPherson. (If anyone were to ask who Alexander was, you could just tell them it's your middle name and pass it off with a laugh saying, "I use both names because I'm a multi-faceted talent.")
If that sounds stupid, note that any used-car salesman will tell you that it's important to find a way to make your name memorable. (Former Car & Driver writer Leon Mandel wrote that during his days as a car salesman, he'd introduce himself to customers by saying, "Mandel's my handle." Corny, but you're gonna remember it, right?)
It seems unlikely that anyone would ask why the name of your business isn't the same as the name on your driver's license, and if anyone did, I'd think it's perfectly legitimate to say, "Because there's already a photographer using that as a business name and I wanted to avoid any risk of confusion." Members of the Screen Actors' Guild have to register under a name that isn't already in use by another member, which is why Iowa-born actress Susan Lewis (for example) joined under the professional name Sagan Lewis.
Of course the hot trend nowadays seems to be to go by one name, á la Pluton, presumably because it gives the impression that you're already as famous as Elvis or Prince or Madonna... or at least that you think you are. Not sure that would work with any of your names, though!
Frivolous aside -- Maybe the next trend could be to invent rapper names; what would be some good ones for photographers? "32 Bit"? "Notorious PSD"? "PJ Slick Summilux"?