The Most Blessed Virgin Mary was, from the first moment of her conception, by a singular grace and privilege of almighty God and by virtue of the merits of Jesus Christ, Saviour of the human race, preserved immune from all stain of original sin.
Pope Pius IX -- Ineffabilis Deus (1854)
That the most holy Mother of God was conceived without Original Sin is an infallible truth, revealed by God.
But this doctrine means so much more than that Our Lady did not bear the sin of our first parents. At Lourdes, the Blessed Mother appeared to St Bernadette and when asked her name, responded: "I am the Immaculate Conception". This doesn't appear to make sense, but yet, I have heard this statement explained as follows:
"Conception" has a much broader meaning than the miraculous biological act of conceiving a child. Conception is a matter of the mind, of the spirit, of the imagination.
We know from the Book of Genesis that when God wills for something to be created, it is created. When He conceives of something pleasing to Him, it is done.
And so, Mary, the most Holy, the one chosen to be the Mother of His Son, in that blessed moment when Almighty God conceived in His mind that this woman should exist, His Immaculate Conception was prefigured until that moment in our Human History when His Immaculate Conception was created in her mother's womb.
So it is perfectly legitimate for the Blessed Mother to name herself "the Immaculate Conception" and for her children to invoke her by that name.