using child name servers

[Rick]

Hi,
Let's say I have a domain such as abc.com which is hosted with a third
party host (i.e. nameservers ns1.xyz.com, ns2.xyz.com).  I then set up
child name servers ns1.abc.com and ns2.abc.com which are mapped to the
IP addresses of ns1.xyz.com, ns2.xyz.com.

Can I now create a brand new domain, efg.com with nameservers
ns1.abc.com and ns2.abc.com?

I am designing some web sites for clients and I would prefer if the
host details are hidden.

Thanks for any input.