For starters, no, you do not need to stir the yeast. Especially when working with dry yeast, one can get carried away and want to stir into the reaction, so that dry yeast tends to bubble up once added to the liquid. Sometimes it may even foam up. But that is not a good idea.
According to expert brewers, it is best practice to leave the yeast be. Dry yeast takes a couple of moments to re-hydrate. So, you can activate the process of rehydrating yeast in your brew itself. This act of pitching smoothens the fermentation process and the whole container mixes alone without the need for stirring. Now, had you stirred the mixture, the yeast would cluster up and the process would have just died.