While Kansas does not list or register DBAs or have statutes requiring or permitting the registration or filing of DBAs or fictitious names, you can reserve a name for 120 days through the Kansas Business Center.
Also through that site you can conduct Business Name Search to ensure the name you want to reserve isn't already reserved or too similar to one that is.
For trademark issues you'll need to search the TESS System through the U.S. Patent Office. For other common questions regarding DBAs and sole proprietorships check out the Secretary of State FAQs page.
Option 3) Get Professional Help
Otherwise, you can work with professional services like IncFile or ZenBusiness who work with people like you and help them start a business in Kansas. They're much more affordable than working with an actual legal team or business lawyer. You may want to consider leveraging their services.
Or, if you do have a lawyer or access to a legal team familiar with Kansas laws, regulations and statutes, contact them and see what other options might be on your table. Regardless, here's to a prosperous year ahead!