Using Pi-hole with a public dns domain

None.
Its just a name.
Make sure to change hostname for Pi-hole to reflect FQDN eg:

Create DNS records at your DNS registrar that needs to resolve for the public.
Create DNS records on Pi-hole that needs to resolve private @ home.

For mail, youd have to create an MX record that points to the server thats processing mail for your domain eg:

pi@noads:~ $ host -t mx dehakkelaar.nl
dehakkelaar.nl mail is handled by 10 mail.dehakkelaar.nl.

Ps.

pi@noads:~ $ hostname -f
noads.dehakkelaar.nl

pi@noads:~ $ host noads.dehakkelaar.nl $(hostname -I)
Using domain server:
Name: 10.0.0.2
Address: 10.0.0.2#53
Aliases:

noads.dehakkelaar.nl has address 10.0.0.2

pi@noads:~ $ host noads.dehakkelaar.nl 8.8.8.8
Using domain server:
Name: 8.8.8.8
Address: 8.8.8.8#53
Aliases:

Host noads.dehakkelaar.nl not found: 3(NXDOMAIN)