Signal doesn't advertise a profile. It advertises a phone number - everything else is data you have locally. It will send a profile picture if you set one but that's it.
- the person is in your own contact list
- you create a conversation with them
- you accept a conversation from them
see: https://support.signal.org/hc/en-us/articles/360007459591
That's what I observe by using Axolotl on the phone and Signal Desktop on the computer.