How do I turnoff my old WiFi network?

> I had to reset my c7110v modem. [...]

   If you say so.  The C7110V is a modem+router, not simply a "modem".

> [...] I how have the old name on my computer under wifi and the new
> name. [...]

   The key phrase there is "on my computer".  Whatever your "my
computer" is, that's where you'd need to delete it.

> [...] How do I delete the old one?

Why not set the name back to what it was before you reset the C7110V?

Visit http://netgear.com/support , put in your model number, and look
for Documentation.  Get the User Manual.  Read.