You will want to register the name that you will be using in business and what your customers will use to find you. How will the mark appear on your letterhead, cards and website? In the scenerio you gave, I would probably register ACME Solutions as a combined term mark. (If, however, your customers will know you simply as ACME, then register that mark.)
You may need to file for an assumed name to use your business name without the "Inc.".
I agree with my colleagues. I will add a few points that may be helpful: Phonetic equivalents are generally indexed under the standard spelling. (For example, "kwic" and "quick" will come up under a search for quick.) The phonetic equivalents will be considered in the analysis of confusingly similiar marks. The answer depends on how distinctive the phonetically equivalent mark is overall. There are many factors used in this analysis. Sound is one of them, but there are many others.
I agree with the other answers, but would make a distinction. If your improvement is non-obvious, and novel, it is potentially patentable as its own invention. The problem is that to practice your invention, you would simultaneously be infringing on the prior patent invention, or require a license from that inventor (or patent owner) to use yours.
Sitting with an experienced patent practitioner is a good idea. First, I find most people misunderstand what the patent covers and make incorrect...
Correction of inventorship in an application is permitted by amendment under 35 U.S.C. 116. The applicant can make a request under 37 CFR 1.48 will generally correct the inventorship in the application in which it is filed. 37 CFR 1.48(a) is directed at correcting the inventorship in an application where the inventorship was improperly set forth in the executed oath or declaration filed in the application.
New York has no rules preventing a Canadian citizen from establishing and owning a US corporate entity such as an S-corp or a limited liability company (LLC). It is also possible for a foreign company to register to do business in New York. These rules will be the same in many states.
I think the decision should be based more upon the business type you are opening. Some states have more advantageous tax rules or other regulatory environments that can be especially advantageous to certain...