Indigenous people have repeatedly requested that non-Indigenous people not use sage bundles for incense or refer to it as smudging / smudge.
There are many other plants that we can use (sage is getting over harvested due to the demand) and the name of the practice is censing.
Palo Santo is also getting over-harvested, please use something other than that, too.
I have never referred to censing as smudging, but I am told that a lot of people in North America are unfamiliar with the word censing, so I thought I would share it.
Some Scottish practitioners have started referring to blessing a ritual space with smoke as saining, but don’t use that unless you are Scottish.
What name do you use? Let me know in the comments.
EDITED TO ADD: white sage (Salvia apiana) used in sage bundles is a different plant to European sage (salvia officinalis).