She calls me by
Call used with by is used when the calling action specifies the person:
She calls me by my first name.
She uses my first name when talking about me or trying to get my attention.
Call used without by is used to ascribe to a person certain qualities.
She calls me Dr.Danger.
She ascribes the quality of bravery to me by using this name.
This does not, of course, apply in every use of the word call, but for the example given and those like it.