Southern don't even "do it the same way" on all occasions. Automatic coach numbers only work when the train knows how long it is - when you have a 455 splitting (it happens), the PIS system has no information on this, so it can't show coach numbers. GTR's Electrostars also can't generally display 3 way splitters correctly, despite much wrangling.
It isn't always. Some TOCs may have tablets/smartphones which let you do something like that, but with many companies, the company-issue phones will only allow you to log formation/CIS issues by phone or email, or a proprietary app which is limited to that TOC only. This will then have to be fed manually into the system by someone else at the other end. It's certainly not compulsory or necessarily even doable at any TOC in my area.