Hello,
I have a Mikrotik router setup by one of our suppliers in our network.
Where's DHCP is already setup and working and the DNS is set as shown in the attached picture.

What i want to setup is to enable to ping a hostname and get a reply.
At the moment, i don't get any reply.
How do i make this possible?

That won't work as a DNS resolver for you unless you tick "Allow Remote Requests"
If you do that then make sure your firewall blocks requests from the WAN.

You should then be able to make static entries and ping them via hostname if you are using the MikroTik for DNS.