Rename data-driven Coded UI test name

So I'm using Coded UI [VS 2013 Premium] to test a very large software.

I'm in the process now of automation one module that is called by 69 different ways. I want to use data-driven testing but I have a problem with the results. The test results outcome does not have a very detailed test name "CodedUITest_1", "CodedUITest_2"...

Is there a way to programmatically rename my test in any way?

I'm currently trying on playing with TestContext but no luck.

Thanks for the help.