Name a phone number without adding to Contacts?
You can use "groups" in contacts. I don't know how to create them on the iPhone, but macOS' contacts app allows this. You should check if iCloud allows this.
https://www.idownloadblog.com/2014/03/01/how-to-create-contact-groups-iphone/
This blog also features an app "Contact Groups".
I am not associated with either the linked website or the said app.