It’s usually called maturation or aging when whiskey is left in a barrel. If it’s specifically being put into a barrel for a second period to pick up extra flavor, that’s called finishing.

Quick terms

  • In the barrel: maturation or barrel aging.
  • Transferred to another barrel after first aging: finishing.
  • The container itself: a barrel is a type of cask.

Simple example

A whiskey may spend years in oak barrels to mature, then be moved into sherry casks for finishing to add extra flavor.

If you want the most natural single-word answer, it’s aging.