A single ticket to Rome is not a single ticket to Venice.

Unless you have no hold luggage (which would be odd coming from BKK), you will have to collect your luggage at FCO, then check it back in at the Alitalia baggage drop, then go through security.

Given that AY and AZ are interline partners, you could request through check-in all the way to VCE at BKK. But in my understanding, Finnair no longer allows this, except for Oneworld carriers, so they will not accept this.