cartodb-postgresql/doc/CDB_UserTables.md

List the name of available tables (only the usable ones)

Using the function

--- Returns a row for each table having given permission with the table name.
--- It also returns tables from others users if you've permission to see them. For example, consider the following scenario:
--- User X and User Y at account C.
--- User X has a public table T.
--- User Y will see table T. 
--- Currently accepted permissions are: 'public', 'private' or 'all'
SELECT CDB_UserTables(perms)

REF: https://github.com/CartoDB/cartodb-postgresql/blob/master/scripts-available/CDB_UserTables.sql