In FortiOS, that is 2 different services: DHCP reservation and private DNS zone.
For the first, you can reserve an IP to a MAC address, right in "Network - Interfaces - <your LAN IF> - DHCP server". Very easy if the device is already connected, otherwise enter the MAC and desired IP address.
Then, you can set up the FGT to be a DNS, with A records for your internal hosts. You only have to make sure the FGT is asked - your devices need to have the FGT as their DNS (similar to having the FGT's LAN interface address as gateway, DHCP server, NTP server...).
You would set up the DNS on your LAN interface as "recursive", that is, if the requested hostname is not found in the local DNS zone, it will be forwarded to the FGT's system DNS. This usually is your ISP's DNS address.
"Kernel panic: Aiee, killing interrupt handler!"