"Regina" or "R" or "The Crown" or "The Queen" is the respondent. These are different ways of expressing the same concept.
However, it is not typical to name "Crown Prosecution Service" in the citation, or the formal heading of the case. This differs from Scottish practice where appeals look like "Adam v HM Advocate". Other public prosecutions can be brought by bodies other than CPS, such as the Health and Safety Executive, so R does not invariably mean the CPS. For England and Wales, the philosophy is that criminal prosecutions are brought by the Crown as the fount of justice, and maintained as such on appeal, and it so happens that the interests of the public are represented by agencies such as the CPS. They are not representing their own interests and are not parties to the case.
We do see "Adam v Crown Prosecution Service" in judicial review cases, which are civil rather than criminal. For example, SXH v Crown Prosecution Service  UKSC 30 was about challenging the CPS's decision on whether to prosecute somebody. An "appeal by way of case stated" may also arise in this way, where there is a point of law to be decided in the Administrative Court of Queen's Bench, such as Chambers v Director of Public Prosecutions  EWHC 2157 (Admin). The DPP is the head of the CPS. The distinction is that a judicial review is about whether the public body's decisions were lawful - they are the ones being scrutinized - whereas in a criminal case, the prosecution is mounted on behalf of the public in general, with the CPS merely happening to be the agency usually responsible. Equally, the CPS can be a party to employment disputes and things like that.
"R (Crown Prosecution Service)" looks a little unusual because "R (Somebody) v Anotherbody" usually means a judicial review on behalf of the Somebody, against Anotherbody, with the R being a vestige of the historical basis for this kind of review. It would be odd for the CPS to be in that position.
If you look through recent Court of Appeal judgements you will see some variations in presentation, but a common pattern of saying something like this:
In the Court of Appeal (Criminal Division)
On appeal from Oxford Crown Court
Mr Justice Glossop
Lord Justice Tibbs
Mrs Justice Bloggs
Mr Justice Dubbs
B Smith (instructed by Appeals-R-Us Solicitors) for the Appellant
C Jones QC (instructed by Crown Prosecution Service) for the Respondent