Yes, you can have the exact same company name as another company registered in another state. You'll have your own EIN, and that's all the feds care about.
If one or the other company objects, they can choose to sue for trademark infringement, or some such.
However, it is common for companies with the same names (i.e. Bill's Plumbing, LLC) to continue operating happily in different states, and they might even benefit from each other's advertising.
thanx for that.