I have a huge data to process, to pace up the work I run multiple MATLAB instances on the same computer. Can it lead to erroneous result as my programs contain variables with same name.
No, but you will be using more memory... And the number of processors you actually have will be shared, so you are not really getting your results much faster. Actually, you might be getting your results slower...
No, it will not lead to errors in the results, but first you must be sure to use a computer with enough memory to handle such "huge" datasets. The fact of having several variables with the same name will only use more memory. I suggest you to try another approach such as parallelizing your calculation, storing your datasets in external tables and workspaces and loading them only when they are necessary, optimizing the code.
there is something unclear in your question. Surely you are not using HPC - Parallel computing machine -. so, some questions: what does it mean that you launching several programs at the same times in your pC? Did you install several Matlab packages? There isn't any conflict among them? You are wasting lots of memory for it (as also Fred Wobus underlined). I don't think that you are speeding up the execution of your programs because the different programs you are running do not share one with each other the results of the computation.
As has been stated before, this is not speeding you up. Also, I don't think you'll get errors in your calculations. If you want to parallelize things manually, I suggest you try to find ways of splitting the data and having your program run on two separate computers. Otherwise, look for the Parallel Computing Toolbox in Google and learn to use it...