I would presume it's like illegal immigrants and the social security system here in the US. You get your social security number, and you have a name. This information, and a few other bits, is saved in the social security system. When you go get a job, you have to give your name and social security number. These may be transferred to a state or national office for verification (in California you have to file a DE34 with the state for each new hire). You can also register to be able to go online to verify name/number.
Usually, the common practice is to get a name/number from someone else who no longer needs it -- they died, or they're too young to be working yet or something. As long as only one person uses a name/number, it's no big deal -- people change jobs, they move to different states, the United States can't possibly track everyone. The problem comes when your name doesn't match your number, or "you" appear to be working in multiple states at once. Working in the same location, probably not a problem -- sometimes people have multiple jobs. Working in different states at the same time? That's a problem.
This is probably how it works for transponders. Starports and space stations or whatever get their updates (and with trillions of ships flying around the speed of updates probably varies correspondingly with your distance from the Core), they check the name/ID and if everything matches then nobody cares. Of course once the ship lands, you can see which ship it "really" is. This is probably how Han Solo became known among certain people -- you might see that the ship is not who its transponder says it is, but unless you have a grudge there's no reason to go alert the authorities -- that other ship's captain might report you if you started the reporting.
If there is a name/ID mismatch, or if the same transponder is flying around the galaxy in multiple places at the same time, it probably takes some time for the authorities in central wherever to notice and respond. I mean, anyone can use someone else's name/social security number. How do you verify that a person is who they say they are? You can't, really, since there isn't a universal fingerprint/retina scan saved for every person. You just sort of have to take it on trust.
A good way to look at it.
