
Bill S. answered 09/26/22
Ivy League Chem Professor, now retired, wants to help you succeed
To answer your last question, the ring is just called purine. I assume you are interested, ultimately, in how such bases may be put into DNA or RNA. There has been a great deal of such research over the last three decades. The general name for such research is studies in nonstandard DNA bases or noncanonical DNA bases. There now exist organisms that contain such nonstandard DNA base pairs as part of their genome. Peter G. Schultz is one chemist who has done a lot of work in this area. For many years it was known that even the AT GC type of pairing Watson and Crick came up with was not the only possible one. Look up Hoogsteen base pairs for another way for purines and pyrimidines to fit together in a double helix. Changing bases is not the only way to make new structures. Replacing the sugar-phosphate backbone with peptide bonds (as seen in proteins) with purine and pyrimidine bases hanging off the chain gives peptide nucleic acids (PNAs). These can bond to themselves or give mixed duplexes with regular DNA strands.
If you are more interested in the rings themselves, that branch of organic chemistry is called heterocyclic chemistry. It is very important because most of the small molecule drugs used in human medicine contain heterocyclic rings.