It should be possible to connect all nanos to the display, just like you would if there was only one nano as long as there is only one nano that actively drives the bus (what ever bus that is). All the other nanos need their bus pins to be inputs (not configured for the bus). So you could have them being inactive by default and only access the bus once they found a matching hash.
But: if multiple nano's are configured for bus usage at a time, communication would be corrupted. In case the display uses a push-pull bus (SPI, UART, ...) this is even electronically an issue, because their bus pins would short the supply voltage and possibly get destroyed. So you need some kind of protection in that case, a current limiting resistor in the easiest form.
As mentioned in comments, the "clean" solution is to have one dedicated controller to be the coordinator.
Some thoughts:
there is a real (not just a hypothetic) chance for bus contentions, because multiple passwords lead to the same hash and you even want to compare hashes for multiple passwords. The occurence of such a collision needs to be expected, though it is not predictable when or if it actually happens.
you probably want to configure the cluster, e.g. to distribute the hash of interest among the Nanos or to stop the cluster when a match is found. Those things would be easier if there's one dedicated master which you can communicate with directly.
the coordinator would always have control over the display. What if you wanted to continously display information on the screen, e.g. a progress bar? That would be difficult to implement afterwards when there's no master.