While Immaculate Heart is most common, Sacred Heart of Mary is also correct. In fact, there are several names for the devotion.
In most theological books written in Latin the devotion used to be referred to as “Sanctissimum Cor Mariae” (Most Holy Heart of Mary), while the Sacred Heart of Jesus was and still is referred to as “Cor Jesu Sacratissimum” (Most Sacred Heart of Jesus).
Later it also became common to say “Purissimum Cor Mariae” (Most Pure Heart of Mary), probably to emphasise Mary’s state of purity as the Immaculate Conception. After the Fatima apparitions it seems that the adjective “Immaculate” (“Cor Immaculatum Mariae” in Latin) became more popular than “Sacred” or “Pure”.
The answer to this is already included in the question. When a Christian venerates Mary he honours her as the most important of all the saints, and as the mother of Jesus. Mary is not a deity, contrary to how a pagan would view, and worship, a mother goddess.
Where do you keep images of Mary? Beside your bed, on your desk, in your wallet?
I had this discussion with a Protestant friend just a few days ago, and I tried to explain to him there is a great difference between worship and veneration. When you are a Catholic you have a firm belief in the communion of saints, of which Mary is the greatest. In the Catholic mind this communion is not some distant theological concept, but a very real part of the faith. In as much so, that the saints become one’s examples in faith and one’s friends in time of joy and sorrow. When it comes to Catholics venerating or praying to Mary or another saint, these prayers are a request for intercession. It is like asking a friend to pray for you.
In the case of Mary, her ‘fiat’ at the Annunciation made her the first Christian. In a sense, this makes her the Mother of all Christians. This explains why Catholics honour her more than any other saint.
In Catholic theology there is a special word for the veneration of Mary, which highlights her unique status and asserts that only God is due worship: hyperdulia. It is defined by the Modern Catholic Dictionary as follows:
The special veneration due to the Blessed Virgin Mary. It is substantially less than the cultus latria (adoration), which is due to God alone. But it is higher than the cultus dulia (veneration), due to angels and other saints.
Have you ever made a pilgrimage to a shrine dedicated to the Virgin Mary?