Having recently swapped my domain over from GoDaddy to NameCheap (using the latter's BYEBYEGD coupon for a bit of a discount), I needed to update my domain configuration on NameCheap with the proper A and CNAME records for Blogger to link to my domain name.
Google provides info on how to create a CNAME record for a custom domain for several registrars, GoDaddy among them, but NameCheap's configuration was less than intuitive to find and update.
I found it from My Account > Manage Domains > Modify Domain, and then under Host Management clicked All Host Records. Then I applied the info in the Google help page to my domain configuration: