We have a domain in SharePoint online as say xyz.com on cloud. Now we have the requirement which cannot be fitted in existing domain. So we are thinking to have new domain as abc.com. I just want to know we have the space on cloud and also we have the domain already so here do we have to purchase DNS for abc.com or what is the process to create the new Domain without the DNS?
Changing the tenant name, either tenant.onmicrosoft.com or tenant.sharepoint.com is by design not possible. There is no button or script that will help you change tenant to tenant2.
What MIGHT be possible is to contact Microsoft via Service Request. They may change the name depending on the new name's availability and probably some other prerequisites, like business reason. The change will affect all site collections. There is no way to have tenant1.sharepoint.com/sites/sitecoll1 and tenant2.sharepoint.com/sites/anothersitecoll in one tenant.
If you need to keep the current tenant for developer reasons (e.g. as a test environment), I'd suggest to contact Billing people about creating a new tenant/subscription and (possibly) transferring licenses from one account to the other.