This is a good bit more detailed advice than Avvo is geared to provide, and really should be done in a face to face consultation with an IP attorney or business attorney licensed in your state, which I take it is UT. That understood, I will give you my take on this.
You started business under this mark with a company registered under your husband's SS#, but you do all the work. You later set up an LLC [same or different name? - it matters!] that you alone own and control.
To solidfy this you want to register the Servicemark of the company in either your name or the name of the LLC. Well, you are missing something - an understanding that common law rights and ownership attach to the first user in commerce of the mark, independent of registration. Here that seems to be the company. So you are going to need an assignment (with goodwill etc.) from the company to either you or the LLC and that may require compensation [we call it "consideration"] from the recipient to the company. My preference in this mess would be to have the assignment from the company to the LLC so it is nominally between business companies and you are legally uninvolved. The companies might make a deal that did not involve any payment so that tax implications might be minimized. Then you should dissolve the company, which you did not mention but presumably would do anyway, so that there is no doubt the good will passed with the assignment. You will want to see a business lawyer in UT, if that is where you are, for all this so you comply with local law and get all the required filings done right. Once the assignment is made then you want a trademark attorney to register the Servicemark in the name of the LLC, I think. I can't see why you would hold it individually and take on personal liability as owner of the mark for the business failings of the LLC under the mark. Seems to me that defeats the purpose of the LLC to insulate your personal assets. However, personal ownership of the mark does give a vehicle for pulling money out of the LLC at favorable capital gains rates, if that is significant for you. Again that is an issue for a business attorney or tax attorney.
There are a number of IP issues that I would expect you are missing, so you might consult with a good IP attorney, unless your business attorney has that expertise or the business attorney's firm has that expertise.
Good Luck, but do get legal representation as that is about as helpful as we can be without knowing details you should not broadcast here.
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If you operate a business as a sole proprietor, then you should be deemed the owner of the trademarks applicable to the business. As that owner, you'd be entitled to file a trademark registration application for that trademark.
But now you've confused me. I don't see where an LLC comes into the picture. As Mr Spock would say: This does not compute.
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You can legally do either. There are good reasons for one and for the other, depending on the factual details of your business.
I have one clothing client to registered in his name and licensed to his company. Then for every license the company grants, he gets the "buy-in" money and the company the royalties. That wouldn't necessarily work for other factual contexts.
Having an outside general counsel already familiar with you and your business will be a big benefit in the years to come.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.