DHCP hostname not working with web_servser_nvm_mpfs example, MPLAB X (v4.15) PIC32MZ

Try to look into the DHCP server tables (router/server that you use in your network) and check the DHCP leases and the host names.
Note that '_' is not a valid name for DHCP host name and it will be replaced by an 'x': look into dhcp.h TCPIP_DHCP_HostNameCallbackRegister() for details.
If you use the DHCP server machine as the DNS server, then it'll resolve the name registered by DHCP.  

You still have not revealed what name you are trying to use.

The router lists a different name because, as before, the '_' character is not valid for a host name. So probably the name should be something like 'MCHPBOARDxE' corresponding to 'MCHPBOARD_E'.
Changing the interface parameters from the web page used to work. I'll do a quick test on my side and let you know.
What version of Harmony do you use and what HTTP server demo?
 
 

Yes, it seems to be a bug, the socket loses its binding when the interface is turned down and the socket is disconnected.
It's been fixed in the repo and it will be part of the next release.
You can apply the fix yourself in the udp.c, around line #2162 in function TCPIP_UDP_Disconnect, it reads:
if(pSkt->extFlags.serverSkt != 0)
{ // stop server connection on the remote port; new rbind needed
pSkt->remotePort = 0;
}
 
It should be:
if(pSkt->extFlags.serverSkt != 0 && pSkt->flags.looseRemPort != 0)
{ // stop server connection on the remote port if not specifically rbound
pSkt->remotePort = 0;
}
 
Please try the fix and let us know if it works for you.
Thank you for finding and reporting this.