Well, the -re ending does seem more natural to me in ordinary circumstances because it's what I grew up with - I would naturally write "centre", "spectre", "fibre" and so on. But when they're part of names, the... fact that it's part of a name takes precedence - I'd always write Trauma Center when talking about the game about a trauma centre.

And seeing as you have to learn American to write HTML and everything, it always trips me up when anyone writing a library of some sort decides that their alignment options are going to be left, centre, right and justify.