Another option is demonstrated by this example:

%sql
 
SET database_name.var = marketing;
SHOW TABLES in ${database_name.var};


SET database_name.dummy= marketing;
SHOW TABLES in ${database_name.dummy};

• do not use quotes
• use format that is variableName.something and it will work in %sql.  I don't know why.  I attached an example from my environment.  I redacted names and data, but you can see that it works with .var and .dummy.  You'll have to trust that I didn't use quotes

FYI: Widget Documentation explains in the blue Note that using the widget method will not work when you Run All or run from another notebook: Databricks widgets | Databricks on AWS