I have created a GUI in Matlab and this is how it looks:

I need to know if I can change the row and column names of the table during runtime and not some static name.
Is there any way to do this or alternatively how can I do this in other way?
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If your GUI is not built using GUIDE you can set / modify the uitable properties like this (directly from http://www.mathworks.com/help/techdoc/ref/uitable.html):
Then you could modify the column names during execution by using:
The only thing remaining is deciding which event will trigger this modification and writing the appropriate callback function. If you could give some details about the GUI it could be useful.
If you are building your GUI via GUIDE, I do not know if it is possible (I guess so but I generally prefer to avoid GUIDE so my knowledge is limited in this area).
UPDATE:
As an example, I wrote a small piece of code that shows this in action. In this case the event triggering the columns names change is a button but it could be anything, hope this helps.