I’m not quite clear as to what you want to achieve. You want the DNS server to obtain FQDNs for the hosts from the ASA which is the DHCP server? Reverse DNS would not achieve this since no FQDNs are stored within the ASA itself. If you look at an example of DHCP bindings in an ASA you’ll see something similar to this:
NWLASA1# show dhcpd binding
IP address Client Identifier Lease expiration Type
10.56.100.11 ff9f.6e85.2400.0200. 1808 seconds Automatic
10.56.101.10 0100.0c29.0505.5a 2840 seconds Automatic
10.56.101.12 0100.0c29.0505.64 2840 seconds Automatic
10.56.101.14 000c.29ed.ff47 3037 seconds Automatic
This includes only identifiers, no hostnames.
I would suggest that the problem is independent of the ASA. It has to do with the ability of the DNS server to resolve the IP addresses to the hostnames of the internal hosts. However, to determine if the ASA is to blame, I suggest you connect a host directly to the same subnet as the Pi-hole bypassing the ASA to see if you have similar results. If it does end up that the ASA is the problem, then you can attempt to permit the appropriate ports. I suggest you take a look at this lesson for more details about that.
I hope this has been helpful!