Name resolution is made by asking DNS server. The RasPi has set default DNS server to ask but of course not your (Windows)DNS server. You do it by editing /etc/dhcpcd.conf
and insert an option
static domain_name_servers=
with the ip address of your (Windows)DNS server. There are examples in /etc/dhcpcd.conf
.
Your DNS server should support dynDNS so it bind the host name to the ip address the host has gotten from the DHCP server. I don't know your environment if this works or if you can make it working. But you have always the option to define a static mapping in the DNS server.