From an identity and branding standpoint, it sounds like your operations in the two states provide the same product or service to the same target demographic. Thus, they should stay as a unified brand as far as your look and feel, including logo, website, business cards, and social media. It's not unusual for companies to co-locate.

This is partially a legal question, so be sure to contact your accountant and lawyer about the matter.

However, it would be helpful to learn more about what your startup does in order to best solve your dilemma, including how location-dependent the service is. Would you like to set up a call so that we can dive into the issue further?