As time passes are you "truly the same person?" There's a compound statement that needs some serious unpacking.
Let's start with the Ship of Theseus, that time-honoured puzzle about identity. As the ship ages, its structure decays. But in this example, each part gets replaced until nothing is left of the original structure. Is it still the same ship? It looks the same. It has the same tonnage and cargo space. It handles the same. It has the same name. Is that enough to preserve its identity?
What then is identity? For Webster, it's "the distinguishing character or personality of an individual." Will that do for now? With identity theft, someone steals what belongs to that person, what he or she owns. Can a thing be owned, be held as exclusive to that person. Perhaps not in some political philosophies, but try to run a functioning democratic state without retaining property rights.
Let's leave that one alone, but can you steal reputation or even life itself? Maybe yes, but that definition would make identity as what belongs uniquely to that person, meaning the person would be impoverished if it was removed. In that case, is time always a thief?
Now back to the ship, and replacing the parts. If the ship is endlessly being renewed, it never ages. By definition, time stands still, meaning that no identity is taken away. The ship, not aging, remains itself, but can there be constant renewal of living things? Probably not or we'd never die.
So now we must deal with the concept of "truly" since this is a word that admits no degree. Sat in that restaurant, the customer's skin continues to flake, changing the person at some microscopic level. Is that change enough to invalidate his passport photo? If identity is a snapshot taken at some point in time, but in a universe where time constantly moves forward, how long is the snapshot valid for? that depends on function,
For me it would be long enough for him to have to honour the bill.