Many shops will give you the option of not taking the hanger when you buy something, they will then reuse these in store. Some charity shops welcome donations of hangers. They may be suitable for reuse through a local reuse network such as Freecycle or Freegle. There are now a large number of reuse groups on Facebook.
Unfortunately plastic clothes hangers cannot be recycled so need to be included in your black/grey waste bin at home or the waste to landfill container at your local Household Recycling Centre. Metal hangers can be included in the scrap metal container.