Stuff gets stolen at airports all the time. And I've read stories on social media about entitled parents/children trying to steal someone else's iPad/Switch while they were traveling, then claiming that it was theirs all along when confronted. And it feels like a TSA agent would believe that it belonged to the crying ten-year-old rather than me.
You could tell him exactly what the device is, what programs/games etc. are loaded to it, and show him that it's your account, not some bawling kid or his opportunistic mother's. But to save yourself from a TSA agent who doesn't know how to work the device, or can't be bothered to check security footage, you can also use a labelmaker to print your name, and maybe some other details for clarity (cheap ones go for about ~20 dollars on Amazon), then stick it somewhere where it's not immediately visible (E.g. on the back of a device normally covered by a case). Alternatively, you could write out you name/details on a thin strip of paper and stick it under transparent scotchtape to make a sort of a makeshift label.
Hopefully you'll never have to prove it, and those cases of entitled parents seem to be the exceptions, not the rule. But if it ever came down to it, you'll be glad that you took the time to do it.