Religious reasons
Catholics who commit suicide cannot be buried in consecrated land (which basically rules out burial in churchyards), and generally could also not be given a funeral service. The same was true for Anglicans until 2017. I couldn't comment on other sects of Christianity, but it's fair to say that this is true for a number of them.
If your relative committed suicide, there's a double-whammy of losing them and of wondering why they felt they had to do it. If on top of that you can't even have a funeral for them and a headstone in the graveyard, and the priest is going to tell you that your relative is going to Hell to burn in eternal torment, that's something no-one needs. So as with so many things, it's very normal (both historically and even today) for people to find ways to work humanely around the inhumane rules of the Church. In the case of suicides, that simply amounts to "don't ask, don't tell".
Suicide methods
For people who gassed themselves or poisoned themselves, the body is probably still in decent condition. If someone has committed suicide in a way which leaves their body in a bit of a mess though - a gun in the mouth, for instance, which takes off the entire back of the skull - then these are details which don't need to be publicised. There's no public interest in these details, only cheap thrills. The family don't need to be told all the details unless there's a real need, and they certainly don't need everyone else in the community knowing.
Or perhaps the method itself is an issue which it would be better for the family if it wasn't shared. Auto-erotic asphyxiation is one thing. Or I personally knew someone who practised self-bondage; we believe they slipped whilst tied and were strangled by accident, rather than intending to commit suicide or practising auto-erotic asphyxiation, but they were still dead. Again, coroners tend to limit what they publicise about these cases in the interests of the family.