Yes. The DHCP protocol supports many varied options for requesting and providing numerous pieces of information to clients. The two most common ones you'll likely encounter are Option 3 and Option 6. DHCP Option 3 is the gateway, Option 6 is the DNS server. See https://datatracker.ietf.org/doc/html/rfc2132 for some bedtime reading.
Amusingly, my Kobo e-reader requests Option 42 (NTP) in the D and R part of DORA, but then promptly ignores the Option 42 response in favour of hard-coded NTP servers in the firmware. This is because Kobo's programmers are morons.