Depending on the local Christian tradition, some Christians prefer to use the title "Our Father," while others almost exclusively use "Lord's Prayer."
In fact, sometimes a Christian who only uses "Our Father" may be confused when they hear "Lord's Prayer" being used as a title.
Most Catholic prayer books refer to the prayer as the "Our Father" or "Pater Noster" in Latin, while the Bible typically has a header that states "The Lord's Prayer."
Both titles refer to the same prayer, but the "Lord's Prayer" is often seen as a title that highlights the authorship of the prayer.
Jesus is Lord
The Catechism of the Catholic Church explains the choice of words for this title in its section on prayer:
The traditional expression "the Lord's Prayer" - oratio Dominica - means that the prayer to our Father is taught and given to us by the Lord Jesus. The prayer that comes to us from Jesus is truly unique: it is "of the Lord."
Jesus is seen as primary author of these words as he speaks them and teaches them to his disicples.
The Our Father also comes from God the Father
The Catechism, however, points out that because God is a union of three persons, God the Father is equally an author of the Our Father:
On the one hand, in the words of this prayer the only Son gives us the words the Father gave him: he is the master of our prayer. On the other, as Word incarnate, he knows in his human heart the needs of his human brothers and sisters and reveals them to us: he is the model of our prayer.
This is important to reflect upon, as God is three in one, never separated, always united. Whenever one of the three Persons acts, all are present. Even the Holy Spirit can be said to be an author of the Lord's Prayer.
The action of the Holy Trinity is a great mystery for us, one that is difficult to wrap our human minds around.
However you name the prayer Jesus taught his disciples, the key is to pray it in faith, praying as Jesus intended his listeners to pray.
It is his prayer, a prayer that provides a model for all of our prayers, whether written in a formula or prayed extemporaneously.