Shades of "Day of the Jackal" in that thought, sir! Such identities would have a finite, if sometimes long, lifespan, as eventually the anomalies ("He can't have been in both places at once") would show up in the data trails. This would be more of an issue in more settled and connected regions like the Solomani Rim; there's parts of the Spinward Marches where you might be able to get away with this for decades.
Circling back to the original poster's question, perhaps it's not so much a matter of destroying the evidence as it is leaving the right evidence - in other words, leaving traces that point to someone who's a real person, but really several worlds away at the time the crime is committed.
