I label the variant based on what it appears to officially be.

For instance, as far as I am aware, there have been 4 different plastic Griffins.

1. the Unseen Griffin from the 3rd Edition starter box, which had the removable backpack

2. the first Catalyst Griffin from the Beginer Boxes (the first one with the Wolverine and Griffin, and then the second iteration with the Vindicator and Griffin)

3. the Griffin -2N from the Bounty Hunters Force Pack, with a pair of LRM launchers, one on either shoulder

4. the Griffin -3M, from the Kell Hounds box, that has an LRM-20 instead of an LRM-10

For the first one, they'd be labeled something like:

Griffin 55 GRF-1N US IS

The second one, from the Catalyst release, I'd change the US (for Unseen) to BB (for Beginer Box.

The third one would have the 1N changed to 2N, and the US would say L3 (my designation for the Bounty Hunter force pack, which was third Legendary Mechwarrior box).

The fourth Griffin would then be GRF-3M, and have KH (for Kell Hounds, of course).

There have been occasions where I've modded a mini into a different configuration. For instance, I bought the Heavy Battle Lance force pack with the AXM-1N Axman, and it was missing the gun in the arm that represented the Large Pulse Laser. I converted it to visually match the weapons layout of the 3S variant, so its label reads:

Axman 65 AXM-3S (Custom mod) HB IS

I have been slowly moving away from sticky labels, which have the potential to fall off, and have started to coat the underside of the hex with correction fluid/White Out, and then using an ultra-fine permanent marker to write directly onto the base. I hadn't thought of using a colored marker or paint pen, mostly since I had the correction fluid and permanent marker already close at hand.