To have an entity on more than one list (i.e. customer and vendor) you have to get around the duplicate name prohibition. Each name must be unique and the simplest way I have used is to append a period to one of the names, preferably the one you will rarely cut a check to (usually customer)
Depending on which one you have in place first may guide you in creation of the second. Do note that my experience also has been that QB ignores middle initials/names so adding that in itself does not make a name unique. Neither does entering a different SS/EIN number.
Here is how two unique names will look
You can add "Jane Doe." as your second name or you can edit your existing name to have the period and then add "Jane Doe" as second name