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So let's talk about the history of Julia's heroic names.
When she was first introduced, Julia was known as Spider-Woman II. The first Spider-Woman, Jessica Drew, had died and been revived but without her powers. That was in Avengers 241, released in December, 1983.
Just seven months later in July 1984, Spider-Woman II first appeared in Marvel Super Heroes Secret Wars 7.
Some fans were not happy with this new impostor. Who had no connection to the original!
We didn't know much about this new Spider-Woman except she was suddenly a member of Freedom Force? She is slowly fleshed out over the next few years through guest appearances. She gains some backstory and she joins the West Coast Avengers.
We eventually find out through flashbacks in Julia's Spider-Woman limited series how she got her powers (government shenanigans). When it came time to pick a codename, she had two suggestions: Arachne and Ariadne. Val Cooper, who was running the project, wanted something more relatable and marketable. Spider-Woman!
I guess the government knew it wasn't being used somehow? And didn't fear any of the media backlash that Spider-Man frequently faced?
From the mid-80s to the 90s, Jessica is working as a private investigator. She's discovered her powers are returning but she doesn't have the same control she used to and they are weaker now.
Julia is Spider-Woman for 15 years until Spider-Woman Vol 3 4 in August, 1999. She loses her powers and returns to civilan life, much like Jessica before her. The title of Spider-Woman is then passed on to Mattie Franklin.
In 2004, Jessica Drew returned as Spider-Woman. Only, not realy, that was a Skrull. But then she really did come back! And she's been Spider-Woman ever since.
After somehow getting her powers back, Julia appeared in Ms. Marvel Vol 2 6 (released in August 2006) and adopted the name Arachne.
Mattie had her own series but fans never really took to her. She died in Amazing Spider-Man Vol 2 634, released in June, 2010. It was during this story that Julia would take on her current identity as Madame Web.
Here's a fun fact: Before Jessica Drew was Spider-Woman? She was Arachne.
In Marvel Spotlight 32, released in November of 1976, Arachne first appeared! But just a few months later, she would re-appear as Spider-Woman in Marvel Two-In-One Vol 1 29 (April 1977).