If they have only just done the purchase they will only have the V5C so might have to wait for the Document to come back in their name before sorting it out.
DVLA phone system is still affected by Covid secure offices I think, and it was always difficult before that.
What about Webchat?
They could try talking to the Insurance company and pre warn them that the number is temporary and will change within a month. If they make a note on the file they may waive the second fee?
My company (Hastings) allowed that last time i changed my car then swapped my plate over.