Earlier quoted context omitted.
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.
What do you mean? You can set a nickname but they'll send your phone number to everyone you chat with? What's the point of nicknames then?
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.