The name Magdalena derives from the term Magdalene, which refers to people from the town of Magdala. Magdala means ‘Tower’, thus the invisible meaning of this name is ‘Tower’.
Magdalena originates from Greece, Czechoslovakia, Spain and Poland (but it is used by many languages including Dutch, Slovak, Danish, German, Swedish and Hungarian). The English variant is Magdalene.
I particularly like nickname options Maggie and Leni, but there are many others such as Alena, Magda, Lena and Dala.