Just don't do stepwise regression. It has so many things wrong with it that it's got an actual FAQ on the Stata website. 

http://www.stata.com/support/faqs/statistics/stepwise-regression-problems/

Good question. First, few things are mandatory in statistics (no one to enforce these things). Often people blindly let the computer run stepwise (and lasso) procedures without considering the meaning of all of the effects that are being added, removed, and changed, and only people do not look for any interactions. 

However, in your situation, how many variables do you have?

If there are no reasons why you should not show it, you need to show it.

I agree with David, but in general your question is unclear. I can't tell if you're asking if it's mandatory to show three-way interactions, or if you're asking if it's mandatory to do so using stepwise regression as opposed to other methods. In any case, the answer to your question will depending on your research design and on the research hypothesis you are trying to test, and you have not explained the latter.

Thanks for the update.

I am using a between subjects experimental factorial design with two factors. These two factors are conceptualised as moderators. Besides, there is an independent variable, a mediator and a dependent variable. So there are five variable in all. The two factors/moderators are hypothesised to moderate the relation between mediator and dependent variable only.

There are two kinds of three way interactions-one between the independent variable and the moderators, and the other between the mediator and the moderators. I am not sure whether they need to be used at all.

With that number of variables, there are a lot of different hypotheses you might be interested in testing. You need to show whichever interactions are relevant to your hypothesis. Since I don't know what your research question is, I can't tell you which particular interactions are the ones you would want to be testing. But generally speaking, your hypothesis will have been about some interaction, and thus you of course need to show that interaction.

Just don't do stepwise regression. It has so many things wrong with it that it's got an actual FAQ on the Stata website. 

http://www.stata.com/support/faqs/statistics/stepwise-regression-problems/

Does that mean that I should not do a three way interaction if I do not have a hypothesis on it?

It does seem that if there is no reason of not doing it, I should show it.

Many Thanks for information about the website. I am too realizing that it is not the best way to analyse, although it is very convenient

Of course, there are many limitations of the stepwise regression.

But the question always is: what are the alternatives?