I'd recommend a brand name.

The 2 of you need a simple "handle". Let people mention you to colleagues and acquaintances as easily as possible. Ensure they know how to get to your site for more information.

Without a single name to mention and find you by, people will get bogged down in a cumbersome explanation – about "an OBGYN and clinical therapist duo who are running workshops for women". That gets awkward. Personal names are forgettable. We all forget the names of people we're introduced to.

Better to have a brand name. Let people mention that. Then your website can do the talking. Apart from being a time saver in actual conversation, this will help the 2 of you seem "established" and reputable. With a brand, you can develop a consistent message by which to introduce your project. Furthermore, you'll be able to separate that project from your own 2 personal identities, which may prove important later on.

Would you like to discuss naming? I have a few ideas. Let's set up a call.