This is a no brainer---you should always register a record company logo or trademark with the USPTO. If you are selling music, you will be selling it nationally and indeed, internationally, primarily in digital format. Therefore, it would be a waste of time and money to file only in the State of Michigan.
I represent many independent record labels, and I am concerned from your question that you have not properly educated yourself on the basics of IP law. If you are going to run a record company, you need to educate yourself on the music publishing and record label business and the IP laws relating thereto.
Finally, you personally should not trademark anything anywhere. You need to retain counsel for this--otherwise you will make legal mistakes that will doom your record label to the fate of the vast majority where the music is never heard beyond the four walls of the recording studio. More generally, anyone starting a record label needs to lay the proper legal foundation by retaining experienced music industry legal counsel---this is what I help people do every day and I promise you that if you do not retain counsel, you are going to screw this up.
Assuming your record company is engaged in interstate commerce in such a way that your trademark is made known to consumers residing in at least one other state then you may register your company's logo with the federal Trademark Office and any state's trademark office where you sell your products or offer your services. The federal registration is more important but there is no downside to registering with the state as well -- and a significant upside in those state's that have trademark dilution protections in their statutes. The cost to register is minimal.
As for your company's trade name it may also be registered as a trademark if it, in fact, serves as a trademark.
You're skipping a step, however. Before even considering registering the trademark rights in your company's name and logo you need to have a trademark attorney "clear the rights" to the name and logo to ensure that your use does not infringe someone else's already-existing rights. And to determine if the name and logo you've chosen are protectable as trademarks. And to ensure that you own the right to use the logo. And lots of other branding matters.
You need to speak with a Michigan-licensed trademark attorney. Good luck.
The above is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
I always recommend registration of trademarks and copyrights with the USPTO. A business can trademark its name and brands if they are not already registered and protected on behalf or another, think about Procter and Gamble, and all of their product names.
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The answer depends on where you are using the mark and/or where you intend to use the mark. If you are only using in the state of Michigan and have no interstate commerce, then you cannot obtain a Federal Trademark Registration. However, with the internet, zero interstate commerce is a rare situation. If possible, apply for registration of both your company name (word mark) and your logo (design mark). This will afford you the broadest protection.
I happen to be a Michigan trademark attorney. Feel free to contact me with any further questions.
Back up a step: Have you done a clearance search? You should not do either until you have done a proper clearance.
If (a) you are using your trademark in interstate commerce and (b) it does not already belong exclusively to someone else, it is already subject to some protection, called "common law" protection.
You are doubtless asking where you should REGISTER your trademark? You shouldn't. You should get an attorney to do that for you. The attorney will recommend registration at the USPTO, since that is national in scope, and confers certain international rights by treaty. State registration will cover Michigan only and will be of limited value if someone else has already registered a mark at the USPTO with which your mark, as applied to your goods or services, is likely to be confused.
You don't "trademark" a business name, you have your lawyer record or register it at the appropriate places.
So, you need a Michigan trademark attorney and likely also a Michigan business attorney.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
USPTO. Search and apply. Rock on!
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Short Answer: By registering with the USPTO you will get national rights, inlcuding in the State of Michigan (by the way, I am very fond of Michigan as an Alumni of the U of M).