If a University change its name after graduation, should graduates use the original or the new name of the school in their CV? Sometimes even countries change their names, again should graduates refer to the original or new names in their CV if that takes place after their graduation?
On a CV I would always put both.
Also in terms of filling out digital CVs where the school auto-populates I would always ask if they prefer I put whatever name they have listed (new or old) or if I should fill in "school not listed" instead. Sometimes I get told to put the school they have, sometimes I get told to put that it is not listed.
(I have had an issue where my college's school name from many many many years ago still auto populates for some reason).
For a CV it is easy enough to list both names. This happened to me. Name the degree (MA, or whatever): University of the South, now named University of the Universe. Give the date of the name change if you like, but I never do. It lets people find you as needed in old records and is completely honest.
This happened to me, and my CV contains the university's original name. I suppose I could add the new name and the reason for the change. (The University of Detroit merged with Mercy College and became the University of Detroit Mercy.) But the current form of the CV, with only the original name, has worked without problems for many years, so I don't see any urgent need to change it.
Your CV is a promotional document, aimed to sell you as an employee, therefore you should use whichever name is best known or most prestigious. If you are unsure listing both is a perfectly reasonable option, but it is probably unnecessary since a google search for the old name will find the new.
Really the only situation where it might cause difficulties for you is if they ask to see your certificates as proof of qualification and the names differ between CV and certificate. However, it seems extremely unlikely that any employer is going to change their decision on whether to hire you or not if you tell them the university changed name and you used the new one when you hand them the certificate.
In my case the institution upgraded status and name. I believe that all graduates were offered a new degree parchment with the new name shown on it. But many of us didn't bother.
In today's digital world where changes of name to an institution become known instantly and many job candidates have their CVs informally verified via e.g. LinkedIn, I would advise you to apply the new name lest someone find no link to that institution on social media and deem you an imposter.
Naturally, keep possession of the old parchment as you worked so hard to get it.