In 4th edition, TMs would always automatically generate a random commcode when they connected to the Matrix.
In 5th edition, your SIN is broadcast through your commlink, which is registered with your SIN. Your (fake) SIN is how you "legally" own everything, without one you can't. Yes, this should mean a TM is incapable of having their Living Persona count as Owner to anything. This is one of the reasons deckers usually have commlinks in addition to their cyberdecks, so they don't have to be using the deck to broadcast their SIN and what not. A SIN is also usually needed to have any kind of bank account, which is why a lot of runners use credsticks-- Otherwise you'd need to empty your bank account every time you switched SINs. In-game, those actions (how you'd realistically have to transfer ownership on everything you own) are all handwaved. See all of the "wtf even is 'Owner'" threads on this forum as a result of Catalyst's sloppiness.
In the end, though? It's a hopeless clusterfuck because 5th edition never thought past the words written on the page, and Technomancers were somehow added to everything as an afterthought.