Hello,
It not not possible to "replace" the C4C URL but you can access your C4C tenant with both the myXXXXXX.crm.ondemand.com URL and an URL like crm.mycompany.com.
You just need to create a dedicated subdomain and a redirection rule on you domain name DNS from crm.mycompany.com to myXXXXXX.crm.ondemand.com
This is usually done in your registar admin tool.
Best regards,
Benjamin