Does anybody know if there are any rules to guide whether to spell a drug compound's name with a simple 'n' or an 'ne' at the ending? E.g. sumatriptan, indomethacin, naproxen, aspirin vs. adrenaline, ergotamine, domperidone...
Yes, there is a convention in the pharmaceutical industry regarding the naming of drugs.
A guide to this is here in Google books.
This is similar to the convention in Chemistry whereby the ending of a chemical name indicates the class of chemical to which it belongs.
However, this is a convention not a rule. Not all drugs are named this way and there may be differences between generic names and trade names.
In your specific question -in, -ine, -on and -one indicate different drug types.
In any case, drug names are proper nouns, and therefore don't necessarily follow any English grammatical conventions.