Well first off, your domain name is not working... says page not found. So you definitely want to get that fixed.
I think you made a big mistake with not finding a company name that you could get a .com domain for. The .us domains are not great and aren't going to present the professional message to your customers. If you had fixedfocus.com then you wouldn't be as caring about this company in the UK. Given where you are at, if you want to stick with that name, then you need to get your site working and get it placed in the search engines. I did a search on Google on "fixed focus" and you didn't show up. That is not good if you want people to find you. You will end up with people not being able to find your site regardless, with the .us domain name... non techie people often assume all sites end with .com and ignore you trying to tell them otherwise.
As others have said, there is no such thing as an international company name, or even a united states wide company name for that matter.
Once your site is working, what I'd recommend you do is contact the owner of the site you mentioned and suggest that they alter their home page to add their location, and you do the same. Then you might both put a link down somewhere down on that page indicating "Were you looking for fixedfocus.us in Florida... Click here" Since you don't compete, it would be good for you both to add that to avoid confusion, although I highly doubt anyone would accidentally hit the .us site until maybe if you get better search engine placement than he has.
I just launched a new identity as Victory Photo and have victoryphoto.com... I had seen many other domains, but all longer... so I had the best and shortest one... which is why I went with it. The one domain I never looked for was victoryphotos.com ... with the "s". Well I just started getting some mis-directed emails where someone intended to send to them and dropped the "s". I've made contact with the owner... and we are going to add the links on our page. He is in Mass and Florida, and I'm in North Carolina, so we don't compete.