Consider talking to the person (with legal advice first). Maybe she'd change her name if you paid for the cost of switching? Probably cheaper than legal action.
After contacting her to tell her that we were already using the name, she went out and registered it on just about every social media platform (that she hadn't already registered) and put up a blog post announcing her "exciting" plans to incorporate our business model into her own.
Have records of your earlier use of the name and your earlier use of the tagline and any other marketing slogans that she is using.
Make a list of all of the social media apps that she has registered using your name after you asked her to stop using it. Contact them all alleging trademark infringement and ask them to shut down the account or rename it.
See if Nolo Press has a book on trademark disputes. If she is using your marketing materials, I think you have good cause for a civil case. I am not a lawyer and this is not legal advice.
Also, build up your business to be better than hers.