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
with the ip address of your (Windows)DNS server. There are examples in
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.