Over the years, Jim has kept tabs on Sherlock Holmes. From his initial research, he found that Sherlock was the younger son of the Baron Mowalter*. Even at twelve years of age, Jim knew you couldn't defeat an aristocrat's son without money and power of your own, and as the scruffy, ill-mannered son of a petty criminal, Jim didn't have a chance against someone like Sherlock.
He promised himself that someday, he would.
At eighteen, he's halfway to that goal – he's the gang's most profitable drug dealer and he's feared throughout London. But in order to truly be able to defeat Sherlock, he needs all records of Jim Moriarty to disappear. He isn't certain yet how this plays into his strategy, but no matter; setting up a false identity can only benefit him.
Ultimately, erasing Jim Moriarty was easier than expected – he never paid taxes or legally owned property, he's clever enough to avoid arrest, and he never bothered with a real ID since he has more fakes than he can count. Within minutes, he's able to hack his old school's server and delete his records. Later, he sends a trustworthy associate to Dublin to destroy his birth certificate.
Jim would like to see Sherlock try to catch him now.
*A/N: I tip my hat to Wikipedia for helping me come up with this title. Check out the List of English Barons. ;)