This is probably only relevant to the UK, because in the USA, PhD funding usually come from the department/university through fellowships/TA/RA.
I applied for PhD at a UK university and got admission. The university also runs an extremely competitive named scholarship competition (for example, this one - not the one I got, just an example) that offer holders can compete in. I was fortunate enough to have won the scholarship. However, I am going to turn it down for a funded PhD at another school.
Is it alright to state that I won this scholarship on my academic CV but turned it down? If this was a typical USA PhD funding offer (fellowship/TA/RA), I would not consider stating it on my CV.
Edit: This is a similar but slight different question from the "duplicate" because I am not asking about the "typical" PhD fellowship/TA/RA that is awarded to candidates admitted to PhDs in the USA. I am talking about competitive/prestigious scholarships like Rhodes and Gates-Cambridge scholarships that one has to apply for outside of the regular admissions process.