The core book was pretty vague when it comes to issues like ownership and personae. Ownership is defined (and I'm away from my books right now, so I'm paraphrasing) as a relationship between devices and grids. Fast forward to Data Trails. One of the things I wanted to do was hammer out the questions about ownership, SINs, and the Matrix. Tying ownership to a SIN (real or fake) would create a pretty disastrous situation for a game in which criminal activity is the norm. Losing a few licenses when a SIN gets burned is manageable. Losing your cyberdeck, less so. This is also why being able to deduce a device's owner simply by looking at it is a no-go. So DT makes a clearer distinction between avatars and persona, a distinction that wasn't quite as clearly defined in other books. If we accept, a priori, that ownership is a relationship between devices and grids, then devices must be able to distinguish between avatars (in the event that two people are using the same stock avatar) and not be fooled by changes to your SIN. First off, I still assume the majority of shadowrunners are SINless, so having a key mechanic hinge off of a SIN is bad design, but people swap fake SINs , get assigned criminal SINs, or just generally find ways of screwing around with SINs. SINs are fluid (for characters) whereas ownership, while not entirely static, is pretty rigid and there's plenty of incentive to create a world in which the players' cool toys don't automatically rat them out in the second session.
The exact mechanic is left deliberately vague, but when you use a device to create a persona, the ones and zeros of the Matrix assemble something that is undeniably you at some level. Your gun knows you, even if you change your clothes. Right now, this element of personae isn't very well understood by the Powers That Be and it can only really be used as a benefit (it makes it harder to steal your stuff or track you down) and not as a weakness. In a very pedantic way, you can't change persona--you can change your avatar and you can change the device you're using to generate your persona (which will make your persona weaker or stronger), but the digital thumbprint of your persona is fixed.