While not changeable in the game itself, it has been possible to change your player emblem in the preview via the Waypoint phone app. (Guide for those who want to try. iOS beta is apparently full.)
There doesn’t seem to be an option to change the colours or background shapes for these emblems, however. I assume there will be more emblems in the final game but if you are only limited to one colour scheme and design for each emblem, then this does seem somewhat restrictive, especially given the emphasis on player expression in other areas.
Will this aspect be customisable in the final game, as it was in Halo games of old? If not, can it please come back?