This too does not sound quite correct. You will only get a browser name prefixed to the result file when you select one of the Executing Browsers, as shown in the attached screen shot, AND your click "Run List". This is normal and deliberate because if you select multiple browsers you will get multiple results. By prefixing the browser name you can tell which browser it was run in. If you leave Executing Browsers all unchecked you get no prefix at all.
The same is true when you use "Schedule Test List". The same logic applies to the displayed results run in this environment. Only the results are stored in the Telerik Storage Service data base, not locally.