On changing phone number; you can also do it on your phone (SETTINGS --> PHONE --> My Number) ... worked for me. It popped up the "carrier may charge blah blah" and the number will also be available for selection in iMessage and Facetime.
**Backstory**
TLDR: Switched from prepaid sim to postpaid sim, but wanted to retain the same number; initially postpaid sim had a different number pre-loaded. The above solution helped me.
My situation was a bit more complicated.
I was on prepaid (SIM#1), and I asked the telco to make me postpaid but still wanted my current phone number PN#1, so they gave me SIM#2, and asked me to wait a few days.
When the day came, SIM#1 got deactivated so naturally I took out the sim and popped in SIM#2.
Forgot to turn off iMessage etc.
When my phone turned on, it detected a different number PN#2 (which came pre-configured with SIM#2); apparently telco had not yet made the full transition (1-Deactivate SIM#1, 2-Activate SIM#2, 3-Transfer Phone number from SIM#1 to #2).
When they did step 3, I had already (mistakenly) activated iMessage and Facetime on PN#2, and did not know how to "refresh" it to my desired phone number (PN#1). Tried restarting, turning on iMessage off and on, resetting network settings (in different permutations of the three).
The only thing that worked was going to Settings--> Phone--> My Number, and manually inputting it.
Afterwards, the desired number appeared on iMessage & Facetime. 😎
In iMessage settings, "You can be reached by iMessage at" still shows PN#2, because I registered it (makes sense). But I leave it unchecked. For PN#1 of course, I tick/check it.
In iMessage settings, "Start New converstations from", it does NOT show PN#2, only PN#1, which I ticked. Because that's what I want to use to identify myself (not my email address) when I send a message via iMessage.
Complicated system, but I like the variety of options for sending/receiving/multi-device-ing. I just wish the number/sim-changing thing was more seamless.