Something similar was proposed for Wellington, possibly in the late 1980s, to be renamed Telford West. This idea went down very badly with some of the inhabitants of the town, who regarded Wellington as being a cut above the rest of Telford and if they had their way it wouldn't be part of Telford at all.
The compromise was to rename the station Wellington - Telford West, and it has now reverted to being just Wellington.
I remember "Wellington Telford West" being displayed at Birmingham New Street on the Solari flapper board many years ago.
Sandwell & Dudley –> Oldbury North
Although the following might be pushing it a bit
Langley Green –> Oldbury East
Rowley Regis –> Oldbury South
I did see in the Birmingham A to Z map around 1983 that Sandwell & Dudley had its original name of Oldbury. It was either in 84 or 85 that it got its present day name, and I recall the West Midlands Travel 87 bus that ran between Dudley and Birmingham via Tividale, Oldbury, Smethwick, Cape Hill, and Dudley Road Hospital used to call in at the station forecourt.
Langley Green I would leave as is, as it is not far from the shooting area and The Merrivale.
Rowley Regis maybe rename to Blackheath (West Midlands) as it is a fair way from Rowley Village, and Station Road that runs nearby has a B65 postcode (Rowley Regis/Blackheath).
The next station through Gosty Hill Tunnel (Old Hill) I would rename to Old Hill and Haden Cross, being as it is a fair trek from Old Hill Cross.
I actually bought a ticket to University in 2020 and I can't remember either. Sandwell & Dudley could definitely go back to Oldbury. After the Brierley Midland Metro extension, maybe Avanti should call at Dudley Port rather than S&D.
I am not sure if the platforms would be long enough for the InterCity trains to call there, and also the canal would be in the way for any required works. I would be in favour of the frequency at Dudley Port being increased when the tram line opens.
Also, Dudley Port could have a modification to its name by renaming to "Dudley Port for Great Bridge".