Specifying a sin has the advantage that one identifies an action and where it went wrong and enables the sinner to work on eradicating that particular action in future.
The Shulchan Aruch recommends specifying sins, but it does not make it a legal requirement (Orach Chayyim 607).
There is a separate issue of whether the sin should be publicised in some way. Here there are two points of view. The Book of Proverbs says, “He who covers up his sins will not prosper” (28:13), whilst the Psalmist says, “A person who covers up sin is to be praised” (32:1).
In the Talmud (Yoma 76b) the first verse is applied to those who sin against other people, whilst the second verse applies to sins between man and God.
However, there is a down-side to publicising sins against others. From one point of view it can encourage the sinner to repent and the victim to forgive, and help to deter the public from sinning.
But on the other hand it might cause embarrassment all round and actually make matters worse. It all depends on the circumstances.
The whole discussion should influence everybody to be careful not to sin in the first place.
My Torah says, “Sin waits at the door and tries to draw you in, but you can rule over it” (Gen. 5:7). I will do My best to seal you in the Book of Life, but don’t leave it all to Me.