Great answer Chris. If I could expand a little, there are some other indicators as well without necessarily needing to place the awarding institution as a suffix.
For example, a D.Phil in the UK is only awarded by Oxford University. I well remember interviewing a research student years ago and stupidly asked her what uni she attended! She gave me a withering look. My youngest daughter had been born hours before and my mind was elsewhere.
Similarly, the ScD is a Cambridge degree in the UK. Every other uni awards the DSc. For my troubles, I’ve got one from the uni I work at plus the other from “the other place”. In the USA, the DSc is often regarded as being equivalent to a Phd and offers no increased job or research prospects. This can be complicated even further by institutions such as Columbia which arbitrarily award both. A UK D.Phil is sometimes looked upon dubiously in the USA as the majority of their uni’s award the Phd.
The third UK collegiate university, Durham, also has some unique degrees. For example, their doctorate in education is an EdD and they have some similarly abbreviated arts degrees.
Then we have the infamous BS/B.Chir and Master’s equivalents in medicine along with MB/BM. In engineering, we’ve got a D.Eng as well as a EngD. There’s a knack to sorting out all these degrees believe me!
Surgeons invariably only declare their Surgery degrees and professional institution membership such as MS and FRCS. Nowadays, they tend not to disclose their MB/BChir or MD/DM on their letterheads.
The other thing I’ve learnt to be wary about is that there’s an increasing tendency not to disclose Batchelor’s degrees nowadays with academics only disclosing their higher degrees. This practice can cause considerable confusion. Years ago, it was rarely seen apart from academic textbooks where degrees were omitted purely for brevity on the title page.