When you change the p-value, the number of differentially expressed genes will change. That in turn, will change every single results in every single type of analysis performed: GO terms, pathway, upstream regulator, drugs, mechanisms, etc. The results will be an entirely different from the results before. Hence, this will be a new analysis. A good thing to do is to analyze your data with a couple of different thresholds and then do a meta-analysis of the results. this way, you will be able to tell whether your conclusions change depending on the threshold used. Obviously, you would place more trust in findings that remain the same regarding of the threshold used.