You can not do this server side (reliably). This is because there is just too much possibility of your traffic being held or buffered on the way: by the webserver, by proxies along the way, by your browser, etc. It would however probably work on CLI.
So I would definitely do it client-side, without sacrificing security (if needed).
If this is only for "cosmetic" purposes, you can create an AJAX method which will return the array of names, and then have Javascript output them with its timers.
Or, you could have AJAX call the PHP script using timers, and PHP will return only one name. It can save the current timestamp in the DB or in a Session variable, and don't return a new name until some time has passed.