Your details are uploaded to the app's server, but they're encrypted using a custom profile key. Signal itself can't see or read them, but your client shares that key with other authorized users, so they can see what you look like and what to call you. Of course, you don't have to use your real pic or name if you want to keep your anonymity. Since you'll still have to verify your account using a phone number, though, you're still not completely anonymous.
Before you activate the feature, take note that your details will be available to all the contacts saved on your phone. You also automatically share your profile when you create a conversation, but you can choose to share or not to share your details when someone else initiates the chat.
Signal says the feature can "dramatically improve the experience in large conversations," but it warns that its beta releases "are not for the faint of heart." If you're ready to deal with bugs and random crashes, you can get Signal beta for iOS by emailing firstname.lastname@example.org and using "Signal iOS Beta" as the subject line. You can also join the beta channel for Android via Google Play.