Using F5 DNS to replace the service provider's DNS

Hello folks:

Please, I hope you could help me with this silly question.

I am planning to get rid out my Internet Service Provider DNS and to deploy the F5 DNS module instead. Currently, the ISP's DNS is responsible for resolving the queries coming to myorganization.com.[my_country_domain] domain. I don not want to use such DNS anymore due to I need to use the F5 DNS module instead. I have deployed the F5 DNS with the same zones and records as the ISP DNS, but I am not sure how to define it in the organization that rules the [my_country_domain] domain. In the F5 box, I have defined an NS record (f5dns.myorganization.com.[my_country_domain] pointing to the LISTENER. Such name f5dns.myorganization.com.[my_country_domain] must be set in the organization that rules the [my_country_domain] domain. But, I am not sure if the f5dns.myorganization.com.[my_country_domain] name is going to be resolved properly as it is only declared in my F5. How the organization that rules [my_country_domain] will know the IP of my name server? Do I need to do something in order to the name f5dns.myorganization.com.[my_country_domain] is known before setting it in the organization that rules [my_country_domain]?

Thanks

Omar