Can Trino choose from which database it will take a table?

Question

I'm new to Trino (the distributed SQL query engine). I want to run the query below in Trino where table my_table exists to all the databases connected to Trino (each database contains exactly the same data-duplicates of the table).

The system consists of a coordinator and two workers on different machines and three databases each one associated with one Trino server.

SELECT * from my_table

Is there a way to run the above query without specifying the database from which Trino will take the data of my_table and let Trino decides alone for this based on query optimization methods?

When I run

SELECT * from cassandra.test_db.my_table

it returns all the data of my_table as expected, but when I don't specify the schema, it returns

Schema must be specified when session schema is not set

As I explained before, I don't want to specify the schema but let Trino decides which schema to use from the available.