It can be. If a girl's full name is Edwina, for example, she might call herself Eddie. However, if you see the name Eddie, you would automatically presume that it's a male name, short for Edward or Edwin. You wouldn't know it was a girl unless someone told you so. The same goes for Charlie, and most other typical male short forms - 99% of the time they are men, but girls sometimes like to choose masculine-sounding abbreviations.

Eddie is a girl's name, however it can be used as boy's name.

Eddie can be a girl's name (Edwina), but is usually a boy's name (Edmund, Edward, Edgar, etc). There's the name "Edie", which has a long "ee" at the beginning, and that is clearly a girl's name. It's short for Edith.

Gender is getting more diverse, and it may one day be obsolete to think there are names for boys and names for girls. One day men will be called India Jade Gaga, as opposed to Charles Philip Arthur George. Cinderella will one day be a transgender beauty who is saved by a cross-dressing princess.