Have Entertainment Questions? Ask an Expert
This agreement does give the company the right to your images and name. This does mean that even outside this production, they can and probably will use the images to promote the company. Now, unless you become famous in the future, they will probably not use your name, but if you do, they may.
I used to sit on the board of a theater company and to be honest with you, this really can't be that detrimental to your career. These organizations are mostly non-profit so money will probably not be made from your name but it may help raise money to give others the opportunity to get into acting. If anything, it will give you publicity to make it easier for you to gain roles in the future, especially if this company feels that you made such a big impact that they want to promote your image and your name.