I'm using the internal wifi (renamed to ap0) as an access point via hostapd and dnsmasq, while the USB dongle and eth0 are meant to connect to available networks and provide a feed-through to the internet when possible. Wlan0 and eth0 do not have any special settings in dhcpcd.conf. The local network here at home also used dnsmasq on my firewall, so I can watch the logs and see all the information that is broadcast with a DHCP request is made.
And no, it wasn't avahi. I was just reading a little about that service this morning since it seemed to indicate this service would broadcast my hostname, however I get the feeling that is something that has to be set up across the whole network, and it seemed like a rabbit-hole that didn't lead to the solution I wanted, so I left it alone.
Ah I think I just figured out the problem though. There is a line in dhcpcd.conf to provide the hostname over DDNS. For some reason I thought "hostname" was supposed to be replaced by the actual hostname, but apparently the line should actually read "hostname <your_hostname>". After a restart it is broadcasting the name via dhcp and I can ping the Pi by name now. The rest of the setup is still working as expected so I think that solved my problem. Thanks for the replies.