In this case it wasn't me who changed it, it was Plack. It does a local $0 = something as a step of a sandboxing scheme when it loads the application code. So I don't have any say in it.
That said, there is a legitimate use case for changing the apparent process name. As perlvar suggests, it's more like a way for signaling state and displaying information than a way to hide identity.
Consider a situation where a number of identical services are running on a host, each in a different container serving a different customer. One is misbehaving, e.g. leaking memory or eating CPU. If I change $0 in them to display the customer name or container id in the process name as a fake argument, the sysadmin logging onto the host can just glance at ps's output and immediately know which of the instances is at fault. I can even display more information in the process name, like the version number, number of active connections, unprocessed items in the queue etc.
Starman, a Plack-based preforked web server also does this, as it displays "starman master" or "starman worker" in its process name(s).