Can we add player’s names to the back of the uniform?

Yes!  USA Volleyball rules do not prohibit the teamname, sponsors, or player's names on jerseys.  The uniform number must be clearly visible and not impacted by any other item on the jersey.  All jerseys must be identical, so if one jersey has a logo/sponsor/teamname then all jerseys must have them and in the same location.  Player names will be unique but must be in same location on the jersey.