When looking at the record, you will see a button that says "edit home facts". As the homeowner, you can "claim the property". It will be listed as an option under that tab.
The public record for my home does not actually list neighborhood, so I'm not sure if it is editable, but it's worth a try! You can edit other facts in that section.
Arapahoe county does have the property listed in Kelly Creek. You can view your record at http://www.co.arapahoe.co.us/Apps/ParcelSearch/PropForm.aspx. Just put in your house number and street name, no directional information.
Hope that help!