Because business names are registered on a state-by-state basis, the fact that a company in another state has the same name as yours is usually not a cause for concern.

However, you are right in that there could be intellectual property issues (namely, trademark) when two companies have the same name. If you have any thoughts or plans for branding your business on a nationwide (and not just local) level, you'll want to be aware of anyone else using the same or similar name.

Depending on the nature of their business and the trademarking steps they have taken, this other company could become an obstacle to you in attaining trademark protection for your company.

As you are already thinking along these lines, you may want to consult with an intellectual property attorney so that you can develop a sound strategy for how to proceed.