What was the reason behind Imam Hussain using "bin Fatima" instead of "Hussain ibn Ali" in his letter to Habib ibn Mazahir, while using the latter in all other letters?
We can't guess the real reason of every act of the Infallible Imam, as they know things which are more than our minds' capacity. Some Ulama in certain matters understand a statement of the Imam is a way which is near to the surrounding circumstances but we can't be sure about the real reason which best known by the Imam (AS)..
Using Ibn Fatima can be to remind certain people that Imam Hussain (AS) is the real grand sin of the Prophet Muhammad (SAWA).
Wassalam.