Your DNS stays where it is
A named Cloudflare Tunnel serves a hostname on a domain whose DNS is on Cloudflare, so using your own domain means moving it there.
Paperboat asks for two CNAME records at whichever DNS provider you already use and issues the certificate itself.
$ cloudflared tunnel route dns api api.example.com $ pb tunnel route add api --name web --to http://127.0.0.1:3000 --wait
$ pb tunnel domain add api api.example.com --route web