Log in to your account at verizonwireless.com; go to Manage Device (if you have more than one device on your account, be sure your device is the one shown, then click Manage Device (Red letters to the right of the device image).
On the next screen you'll see your device, and the device name - this (as you said) should be correct. Scroll down below the image to several choices under Manage Device and click on Share Name ID.
That is where it probably says "Nicola". Edit that to "Nicole" or whatever you want the caller ID to show, and scroll down to SUBMIT.
Where are you (or others) seeing it show as "Nicola"? Does everyone see this as the caller ID? Perhaps someone has mistyped your name in their contact list, so when you call it shows as "Nicola"?