Deirdre was a tragic heroine in Irish myth. So her name became used to symbolise or personify
Ireland itself - like
John Bull,
Marianne, Uncle
Sam ... and so you get whole literary works (like
Deirdre of the Sorrows) with a hidden meaning. Irish history having been pretty miserable, the meaning of sorrow and misery has been firmly associated with the name.
Must say, I would expect people to give their daughters a name less obvious than "woman" and less gloomy than "sorrow", but who am I to judge? It sounds beautiful. And my friend was widowed as a very young, pregnant wife, and when her daughter was born she named her
Deirdre. It seemed appropriate then, all right.