No, you don't have to have a company to register your trademark.
For most entrepreneurs, it's more advisable to have their company be the owner of the trademark, but there are cases where individual ownership might be preferable. For example, a business owner might want to secure intellectual property rights while setting up a new company. Or, an individual (e.g. a celebrity) might purposely wish to retain ownership rights and license the use of the trademark to a different company.
For individual-owned trademarks, it's common to draw up this additional license agreement between the owner and the user, even if it's your company. Another option might be transferring the trademark ownership to the company once it's set up.
If you want to learn more about the advantages and disadvantages of registering a trademark as an individual, we have written an article on the topic.