To rename a local BDE table, choose Table | BDE Utilities | Rename.... Related files (index files etc.) are also renamed. Note: this way, you cannot change the table format (e.g. from Paradox to dBase), you should use data exporting for this.
To rename a table in SQL-based databases, use a SQL query according to your database documentation. For example, to rename a PostgreSQL table, execute the following database query:
ALTER TABLE <old_table_name> RENAME TO <new_table_name>