Joining a project does expose some identifying information about you to the group project administrator. It may also expose non-identifying information about you through the project's Public Project Website (should it have one).
The group project administrator can see your results. They can view some of the information listed in your myFTDNA account such as your contact information. The group project administrator will not be able to see your password.
Projects often set up a website on which member results are posted. How these results are identified is up to the group project administrator. Results are often listed by the participant's oldest known ancestor, kit number, or last name. You may wish to discuss what information will be available on the project's website before joining a project.