BIND Alternatives
BIND is described as 'Is by far the most widely used DNS software on the Internet. On Unix-like operating systems it is the de facto standard. It provides a robust and stable platform on top of which organizations can build distributed computing systems with the knowledge that those systems are' and is an app in the network & admin category. There are more than 10 alternatives to BIND for a variety of platforms, including Linux, Windows, Mac, Self-Hosted and SaaS apps. The best BIND alternative is Unbound, which is both free and Open Source. Other great apps like BIND are dnsmasq, PowerDNS, WireHole and CoreDNS.

As far as I know, dhcpcd's only relationship to DNS is that it makes the DNS server's IP address available to the host on which it runs.