They have a feature called "sealed sender"[1]. Your Signal client authenticates to a Signal service that verifies you, and then signs and issues a certificate that you can use to vouch for your identity.
Then, you can encrypt this certificate as part of your message. Then ask Signal to deliver your message to the recipient. The Signal server won't be able to tell the recipient the account that the message is from, but after the recipient decrypts the message they will see the signed certificate and know it was you.
The problem with this is, Signal is centralized and they see the both the IP address (and other metadata) when you contact them to obtain the certificate and they they also see the IP address you send the message from. Correlation between the two Signal-operated services would reveal your identity. Unfortunately we, as users, have no way to know that this is not happening.
Then, you can encrypt this certificate as part of your message. Then ask Signal to deliver your message to the recipient. The Signal server won't be able to tell the recipient the account that the message is from, but after the recipient decrypts the message they will see the signed certificate and know it was you.
The problem with this is, Signal is centralized and they see the both the IP address (and other metadata) when you contact them to obtain the certificate and they they also see the IP address you send the message from. Correlation between the two Signal-operated services would reveal your identity. Unfortunately we, as users, have no way to know that this is not happening.
[1]: https://signal.org/blog/sealed-sender/