two theories as to the name green card.
1. Years ago, almost every country on the planet used green cards for these 'resident alien' cards.
2. people with 'resident alien' cards were considered to be 'green' (as in new), so their 'resident alien' cards were called 'green' cards
Since no-one can remember the green cards being actually green way back (mine was, I believe blue in 1965 in the USA), I tend to believe it's number 2