My PC says the same for “ping wiznet”: Ping request could not find host wiznet. Please check the name and try again.
and does it for simple reason - there’s no host with “wiznet” name in the internet and in my local network.
Logically you need to implement DNS query on your W5500 to be able resolving host names to IP addresses.
Then your question is not related to the WIZnet but rather to administration of the operating system of the PC or of your network in overall. You can put the required name into local DNS if you have such, or into hosts file on the PC so that PC can associate host name to IP locally.