Trademark applications and registrations can be owned by an individual or by an entity (e.g., an LLC, LP, corporation, etc.). The question of whether to file in the name of an individual or an entity is really one of intent. Do you intend to own and control the trademark in your individual capacity, or do you intend for an entity to own and control the trademark?
To avoid creating a legal mess, decide what makes the most sense for you (individual ownership or entity ownership), file an application for registration in the form you choose, and and be consistent in how you represent such ownership to others.
Assigning a trademark from an individual to an entity (or vice versa) after a trademark application is already filed will at the very least involve additional cost. Also, if the application was filed on an “intent to use” basis, you may not be able to assign the application unless you first file a statement of use or amendment to allege use by the original applicant.