Just to bring back this thread I have the exact same issue. I replaced a crappy ISP Plusnet router for a client with a v2862 and now local DNS resolution doesn't work. They have a local app that points to a SQL database using 'hostname' which no longer works. From doing some googling it appears Draytek rotuers act as a DNS proxy rather than a server, even though my home Sky router can perform this function.

Anyway, I added the hostname as a LAN DNS Resolution entry but I could still only ping by adding a full stop at the end eg 'hostname.'. I just tested by adding a CNAME and it worked without the . so thank you for the tip.