We learn from Acts 11:26 that the disciples of Jesus of Nazareth were first called "Christians" in Antioch, most likely in the thirties of the first century. Originally a nickname, "Christians" spread quickly and became the proper name of those who believed in Jesus as the Messiah.
While it is allowed, for a good reason, to celebrate the Chrism Mass on another day, there are good theological reasons for celebrating it today, Holy Thursday, as normal practice.
Our name "Christian" still carries the meaning "followers of Jesus", people who claim that he is the Messiah, Christ. Hence we bear Christ's name as a profession of our faith in him. Yet our following of Jesus as his disciples means much more to us than simply a teacher-disciple relationship. Our name both signifies and demands, a deep interior relationship with Jesus as our personal Lord and Saviour. Jesus was the Christ, the Messiah, the one anointed by the Father for the mission of saving us all. Hence we, his followers, are also anointed, in Baptism and Confirmation, with the sacred oil that makes each one of us "another Christ", a Christian.
May the Lord bless all Christians with the fullness of his love that we may more effectively work for the spread of the Gospel and the coming of the Kingdom.