Any individual, company, or association can own a trademark. Sole proprietors, partnerships, limited liability companies, corporations, trusts, and estates can all hold trademark registrations. A trademark can also have multiple owners.
However, there are additional costs associated with transferring the ownership down the line, and so the practical question is whether the trademark should be owned by the individual founder or by the company. Tying ownership to the company simplifies commercial use, enforcement, and eventual sale of the business. Individual ownership can make sense where the person wants to retain personal control over the brand, such as a professional licensing their name for merchandising.