Lower self-reported transphobia was associated with a 66 % reduction in ideation, and an additional 76 % reduction in attempts among those with ideation

https://bmcpublichealth.biomedcentral.com/track/pdf/10.1186/s12889-015-1867-2.pdf

An increase by one context in which a chosen name could be used predicted a 5.37-unit decrease in depressive symptoms, a 29% decrease in suicidal ideation, and a 56% decrease in suicidal behavior.

https://www.jahonline.org/article/S1054-139X(18)30085-5/fulltext#intraref0010a

Socially transitioned transgender children who are supported in their gender identity have developmentally normative levels of depression and only minimal elevations in anxiety, suggesting that psychopathology is not inevitable within this group.

https://pubmed.ncbi.nlm.nih.gov/26921285/

So yes. Increased depression and suicide among trans people is, according to the research, entirely correlated with social factors like how much they are accepted by friends/family and chose name use.