Changing the name of my LLC (or starting new one) vs. doing a DBA

Hypothetical situation:

Say I have an LLC for a snack and soda vending machine business. I want to buy some real estate through the LLC versus setting up a new LLC (or changing the name). I want my future tenants to write their rent checks to Affordale Housing Solutions versus Affordable Snack Solutions.

All of the above names are completely made up, but you get the point. Can I just file the paperwork with the SOS to set up a DBA through my current LLC? Is there an advantage/disadvantage either way?