It's called dignified death because you can decide to end it before your body wouldn't allow you to feel or project dignity anymore. There are situations that make us "uncomfortable" (what a euphemism) in social setting: losing your ability to control your bowel movements, or urination, or endless shaking, or screaming at family you don't recognize, etc... Some people would rather not have others (often loved ones) be witness of this so they can keep a "good mental image" of the person in their hearts and minds.
If you know you have a brain degenerative disease that is likely to end up in you screaming mean things at your loved ones, you may want to spare them the pain and trauma of seeing you like that.
That's what the dignity part of it is about, in my opinion, but people do have various opinions about what it means, as evidenced by answers recorded here:
https://www.deathwithdignity.org/news/2017/07/death-with-dignity-means/