When someone refuses to use a trans person’s new name because of their “beliefs”, that’s them effectively saying “my beliefs are that I know who you are better than you do, so you’d better conform to who I think you should be”. Trans people commit suicide not because of the name, but because of what refusing the name really means: that society wants to define their identity, denying them the personal autonomy to define themselves. I think if you denied such autonomy to cis people, plenty of them would commit suicide too, because living as an identity someone else has chosen for you is intolerable to most humans.