Yes this is possible. You'll need to set up the cname – here are some docs to get started with this if needed.
Then point the Raygun client at your web address by setting the
apiEndpoint option to
clog.mywebsite.com in your Raygun initialisation code.
For example, in our .NET provider it would look like this:
<RaygunSettings apiEndpoint="clog.mywebsite.com" />