Health › checks. Pick DNS name resolves. The agent asks its own resolver. You are still pushing a document, not a script.
Open the machine, then health › checks. The primitive is DNS name resolves. Hostname is the name this machine should be able to look up. Expected IP is optional. Here fs01.example.local must come back as 10.1.1.20, so a stale hosts entry or a bad DNS server fails the check. Add a disk or ping check is the same editor.
Press add to list. The check sits in the document. Push to agent is the next click, and it asks you to confirm. Push replaces the whole document. This shot stops before that, so nothing has been sent. When the name does not resolve, or resolves to a different address, the alert is a check failure.
Push is a two-step button. The agent must be online to evaluate. You can still add the check while it is offline, and it applies at the next hello. A ping of the same host is Add a disk or ping check. Reaching a port is Check that a share or port answers.