Most of them are caught through address/wallet connections. Addresses that have been used together in a single transaction are flagged as belonging to the same wallet by services such as walletexplorer.com, while some blockchain explorers like blocktrail.com are able to crawl bitcointalk for mentions of specific addresses. Proof gained this way is usually irrefutable.
Other than that, it's just circumstantial stuff like post patterns, etc. but those are a lot harder to prove. People with multiple accounts also tend to not post very well.
As for whether you can report them or not, yes. There's an entire thread dedicated to that
here. Make sure you have proof before accusing someone though.