It depends on the systems and the network settings at your ISP. The systems that ISP's operate are too numerous to mention. Some operate almost all their server programs on one very powerful (UNIX-) machine, others operate a network of many computers that are basically pc-type hardware.
Some use Linux/Unix operating systems other Windows server systems (and some mix it!). And ISP's vary in size from 200 customers to 2.000.000. They can't all operate the same systems!
But the general answer is that probably the ISP operates some nameserver internally. Such nameserver will typically be configured with the some name like 'mysqlserver' pointing to the ip of the mysqlserver on the local network.