Signal would have to change how they work for that, at present it shares your profile name after you've initiated a chat using the "username" - very confusing choice of wording.
> Usernames simply allow you to initiate a connection on Signal without sharing your phone number
> Starting soon, your phone number will no longer be visible to people you chat with on Signal, unless they have it in their phone’s contacts. You will also be able to configure a new privacy setting to limit who can find you by your phone number on Signal. And, you’ll now be able to create an optional username that you can share with the people you want to connect with on Signal.
As far as I can tell, "limit" will soon mean "disable". They just can't flip that switch yet given that legacy clients will not know what to do about "numberless contacts".
> do not get my phone number period
I'd also like that, but they apparently use phone numbers as a primary key for account recovery and identification (e.g. on a new device without the old one present), so that's probably very hard to change architecturally.
There are some interesting concepts of "identityless messengers", but this is inherently hard to do on mobile – at least the platform operator will always know which identities are clustered together on a given device if you want efficient push notification delivery over APNs/FCM.
Currently everyone who chats with me cannot see my phone number — even people who have my phone number saved in their phone (I was surprised as I thought it would still show this if they had it saved). There is a setting to entirely hide your phone number from everyone.