You can't request it. You can make sure that the box in settings is ticked to allow moves; if you are on mobile you may need to contact support to verify this, but it is "opted in" by default, so if you haven't done anything to change it you should be opted in.
When conditions are right for you to be moved to a new neighborhood (they have to find a more active neighborhood to which to move you with a hex that matches your boosts), you will be moved on a Monday (everyone moves on Mondays that will be moved).
When I started I was literally at the edge of the map, and I was moved after about 4 weeks of play.
If your map is only mostly dead and not entirely dead, that may be as good as it gets. After my move I have a handful of active neighbors.
If you haven't already, join an active fellowship. Your fellowship will make a much bigger difference in your gameplay than your neighbors.