Ideally, you should ensure your business/brand name is available to be trademarked before you fall in love with the name.
Trademarking your name will help you build a strong brand and ensure that no one can rip off your brand!
You should also make sure to protect your other brand names, logos, and slogans with a trademark. This may be a product collection, course name, signature services, etc.
You should budget long-term to protect all brand identifiers that are generating (or will generate) revenue for your business. You should work with an experienced IP (intellectual property) attorney to conduct a trademark availability search and to file a trademark application.
Even when working with an attorney, you should search the trademark database (tmsearch.uspto.gov) to catch obvious trademarks PRIOR to paying the attorney to do a search. This can help catch the low-hanging fruit and leave the in-depth search to the attorney so you get the most value for your money.
In the US, most trademarks are filed electronically through the Trademark Electronic Application System (TEAS).
Additionally, at this point, you should have an attorney do an IP audit to map out what trademarks, copyrightable works of authorship, and patentable inventions/methods you have in your business + how to protect them.