Transferring data from iPhone 5C iOS 10.3.3 to a used iPhone X iOS 12

I have obtained a used iPhone X from a family member who has misnamed the phone before transferring it to me and they did reset the iPhone themselves and I am trying to correct that. I have successfully changed from a former Apple ID that they left on the iPhone X to my Apple ID though in the Apple ID screen the phone is still named under the former name.

I did not do a reset of the iPhone X prior to entering my Apple ID information. Is it necessary that I should have done that before setting up my Apple ID and naming the iPhone X?

I did sign onto our home WiFi (but have not transferred or obtained a new SIM card for phone service) and since the WiFi connection my Apple email is now available on this iPhone X. When I swipe right I do see some of my Calendar information, however when I do tap the Calendar and Notes icons I see an information window that informs me of changes to these 2 apps.

Did I enter my Apple ID information too since I did not reset the iPhone X?

I am also in the process of doing a iCloud back up of the iPhone 5C as well as a iTunes back up done yesterday.

Thank you for any and all assistance in this matter.