According to [reddit](https://www.reddit.com/r/MonsterHunterWorld/comments/d2173k/player_name_color_meanings/):

> Green is after story. Orange is for completing HR100, Blue is for entering MR, Purple is for clearing MR story.

> MR200 is yellow

It's an indication of progress. Each of the quests to unlock the colours are optional, and are unlocked once you have passed that point in the game. For example, the MR200 quest:

> Apparently you need to do all the optionals that upgrade equipment like the mr 150 and mr 175 quests to upgrade mantles, to unlock it.