Performing wildcard search using the json_contains function in mysql 5.7 and above
You can use JSON_SEARCH with wildcards:

SET @j = '{"MyName": "FirstName LastName"}';
SELECT JSON_SEARCH(@j, 'all', 'FirstName%', NULL, '$.MyName');


Will return the path: "$.MyName"

If you want to filter by this, use an alias and check it in a HAVING clause:

SELECT JSON_SEARCH(`json_col`, 'all', 'FirstName%', NULL, '$.MyName') as `search`
FROM `users`
HAVING `search` IS NOT NULL;


or.. in a WHERE:

SELECT *
FROM `users`
WHERE JSON_SEARCH(`json_col`, 'all', 'FirstName%', NULL, '$.MyName') IS NOT NULL;


https://dev.mysql.com/doc/refman/5.7/en/json-search-functions.html