If you transfer domain to Namecheap or any domain name registrar, the nameservers associated with the domain will remain the same i.e won’t automatically change to Namecheap nameservers.
If the nameservers are that of your previous registrar’s default DNS service, the transfer process may cause temporary downtime of your website and/or email service interruption because the old Registrar’s nameservers will stop responding to any queries for your domain name.
Hence, if you transfer a domain name that is currently mapped to a blogspot blog to Namecheap.com, you are required to change it’s nameservers to Namecheap nameservers else the Blogger custom domain will stop working. If you don’t know how to do this, follow me through the steps below :
Sign in to Namecheap.com, select “Domain List” from the left sidebar and click on the Manage button next to your domain:
While on the “Domain” tab, scroll to the “Nameservers” section.
Click on the dropdown arrow, select “Namecheap BasicDNS” and click the “save icon” next to it.
Click on the “Advanced DNS” tab and click the “Add New Record” in the “Host Records” section
Select “CName Record” in the “type” drop down.
Type “www” in the “host” field
Type “ghs.google.com” in the “value” field and save as seen in screenshot below :
Add and save the Blogger 4 “A Records” as seen in the screenshot below :
Your domain should start working after some hours.
I hope this helps.