The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Use UNION ALL instead of UNION (query line: 17): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `AnotherTable` ADD INDEX `anothertable_idx_subjectid` (`SubjectID`);
ALTER TABLE `SomeTable` ADD INDEX `sometable_idx_subjectid` (`SubjectID`);
ALTER TABLE `YetAnotherTable` ADD INDEX `yetanothertable_idx_subjectversionid` (`SubjectVersionID`);

The optimized query:

SELECT
        'SomeTable' AS tname,
        COUNT(*) AS ttlRecords 
    FROM
        SomeTable 
    WHERE
        SomeTable.SubjectID = @SubjectID 
    UNION
    SELECT
        'AnotherTable' AS tname,
        COUNT(*) AS ttlRecords 
    FROM
        AnotherTable 
    WHERE
        AnotherTable.SubjectID = @SubjectID 
    UNION
    SELECT
        'YetAnotherTable' AS tname,
        COUNT(*) AS ttlRecords 
    FROM
        YetAnotherTable 
    WHERE
        YetAnotherTable.SubjectVersionID = @SubjectVersionID