"Asylum" is an example of what was a positive label, adopted for that reason, which has lost that quality largely because the places themselves didn't live up to that positive intent. That has often happened.

But in any case the large places which were charmingly referred to as "Lunatic Asylums" have ceased to be the way people with mental illnesses are treated, and carrying over the term "asylum" to use for the small units where people with mental illnesses are treated would be misleading.

Changing names and using positive language by itself doesn't make any real difference, and it can camouflage horrors at times. (For example "Arbeit macht Frei" on the gates into Nazi death camps). But changing names as part of a change in the way people regard other people is something that can help.