There's dif ways to initial your bags. And a million places to do it!
You can heat stamp them, so just the impression is left. Or, you can have it heatstamped with a gold or silver coloured foil to match the heardware of the bag. From what I understand, they aren't crazy about mixing hardware colours, so if ya got gold, they'll give ya gold foil. OR, a somewhat more traditional method - they can place small metal letters on your bag that are simliar to brackets. You can have this kind removed the easiest from what I understand, but the indentations from the metal fasteners will always remain, so best to place YOUR initials on the bag then, in the same place.
There might be other ways to initial your bags, but these are the only ways I'm familiar with. I have met craftspeople who make you swear up and down you really want them... in case a married gal decides she wants out, her initials on that bag are for keeps!
(ETA: foil CAN be removed, but I don't think the heatstamps can be altered. HTH)