You can't use an index for your case statement, because it can't be rewritten and i doubt, that any DBMS will use an index for that.
Anyway, your example should use an index, because renaming a calculated column to the original columnname is bad practice: "Where TRN_NM = '0066563438'" uses the base column TRN_NM, but not the result of the CASE
SELECT 'blabla' AS databasename FROM dbc.databases WHERE databasename = 'dbc';
*** Query completed. One row found. One column returned. *** Total elapsed time was 1 second.