What's in a name?

If a computer gets a new shell, does it need a new name?
Clearly it's important that the computer have a name.
And it just wouldn't be right to have two computers with the same name.
(They become terribly confused. I once accidentally christened a second computer "whitestar"
and it promptly developed defective RAM.)
The computer in question is my oldest laptop.
Not the first, but now the oldest.
Its name is (was?) My Laptop,
because this uniquely identified it as the only portable computer in our apartment.
My Laptop has been to three countries (and three offices) on two continents
over the course of four years
and has seen all generations of RedHat since 6.
Something rattled inside the case if you left in on too long,
and the battery didn't really charge much anymore
and grease on my fingers had gradually worn away the letters on the keyboard
(so I think you could probably tell my password from just looking at it).
It had cat fur stuck on the outside because CM spilled a coke
and then sat on the computer (because even though this is sunny California
my cat likes the warmth of a computer fan).
So when the fan stopped working last week, and My Laptop wouldn't boot,
I took it for dead.
I took it into the office to recycle it, but they had a spare T23 shell on hand
(all the parts except the hard drive)
so they took the hard drive out of the dead, rattling case
and put it inside a shiny new body.
It's just like nothing ever happened to it
(except it's sprouted more memory and a builtin wireless card).
But is it really the same computer?
Does My Laptop need a new name?
It probably should get a new password.