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.