Interestingly in modern times, at least in conservative areas, sometimes police/coroners will label an accidental self-hanging as suicide, as that's less embarrassing to the family than the reality.
A friend of mine took his own life. The obituary said sudden accident. It's what his family will say in most situations. But they know.
It would be very twisted to keep relatives in the dark, though I'm sure someone has done so and thought it a kindness.
Suicide means the deceased did something to end their life, and had the intention of ending their life when they did it.
Misadventure means the deceased did a risky thing and died, but did not have the intention of dying when they did it.
Accident means the deceased was doing a normal activity and died.
Definitions of the manner of death can be nice and clear on paper, but are much harder to apply to the situations of a person's death, so there's lots of overlap between suicide and misadventure. It's often difficult to show intent, and so those deaths sometimes get called misadventure, or they have a narrative conclusion.
I've actually read an interview with a parent who lost a child that way who said it gave them comfort knowing that their child's death was simply an accident, rather than a mental illness problem that they could have missed.
Wish I could remember how to google it and get an actual cite. IIRC it was in the New Yorker or something.
Sort of like the precipitous decline of alcohol-related deaths during prohibition: clearly prohibition must have prevented (or delayed!) some alcohol-related death, but out of respect for the family another cause of death was commonly used instead during that period.