Correct, Mary Magdalene was not Jesus' mother.
Luke does not mention Mary the mother of Jesus by name at the scene of the crucifixion/burial, but he does refer both to her and to Mary Magdalene in various places in his work, and refers to them distinctly (compare Luke 24:10 with Acts 1:14).
Note that while in Matthew & Mark, Mary the mother of Jesus is not mentioned by name at the scene of the crucifixion, both indicate that there were multiple women named Mary present. Mary (the same name as Miriam in the Old Testament) appears to have been the most common girl's name for Jews of that region in the first century--see Bauckham's work Jesus and the Eyewitnesses.
It may be helpful to disambiguate 7 different women in the New Testament named Mary:
- Mary the mother of Jesus, wife of Joseph, from Nazareth
- Mary Magdalene, (probably) the first witness of the resurrection, from Magdala
- Mary of Bethany, sister of Martha & Lazarus
- Mary the wife of Clopas (or Cleopas), a witness of the crucifixion
- Mary the mother of James & Joses, a witness of the resurrection (possibly the same person as #4)
- Mary the mother of John Mark (see Acts 12:12); her home in Jerusalem was apparently a meeting place for Christians. Her son traveled with Peter & Paul and repeated patristic evidence indicates that he wrote the second Gospel
- Mary of Rome (see Romans 16:6); we know precious little about her.
See a source for this information and more detailed discussion of the 7 Mary's here.