She owns the trademark if she uses the trademark in commerce. Registration is not a requirement to be the owner of a trademark. Contact a lawyer to discuss your situation, but my guess is you'll be choosing a new name.
Pick another name. If she is using it in commerce, she owns it and you will be an infringer. Ownership arises from first use in commerce or from application for federal registration, whichever is earlier. Since you say she is earlier, you are very likely to lose this conflict. Use of a servicemark on a commercial website or commercial FB page is very likely valid use sufficient for her to own rights to the servicemark. Consult an IP attorney to help you select a better servicemark or trademark.
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.
Just because a person has not "officially" applied for a trademark does not mean that that person does not have superior rights to that trademark. By applying for a mark you are aware is being used by another is wrong and, ultimately, that other person should prevail. You should immediately cease using the mark lest you be liable for infringement and subject to damages and attorney's fees. You need to select another name or find yourself involved in potentially costly litigation which you could ultimately lose..
My colleagues offered good insights here.
I would add that whenever you endeavor into investing in a trademark it is very important that you conduct the proper clearance due diligence upfront and before you submit an application to the USPTO. In the US, this means searching under both federal (USPTO) as well as common law because trademark rights stem from use in this country NOT registration. This means that acquiring a federal registration does not necessarily mean that you are not infringing on another's intellectual property. See the link below for a detailed explanation of the due diligence process and a guide on how to choose a strong trademark.
I suggest that you consult with a lawyer in private and discuss your objectives in more detail. You can start by calling around to several for a free phone consultation, get some insights then pick the best fit to work with.
DISCLAIMER: this is not intended to be specific legal advice and should not be relied upon as such. No attorney-client relationship is formed with the law firm of Natoli-Lapin, LLC on the basis of this posting.
If she is using the name in connection with her books, she may have trademark rights to the name even though she has not filed a registration. You probably need to go with a different name.