What should we say when someone asks 'What is your religion?' Recently I faced such thing. Occasionally I faced an orthodox guy. We were talking about marriage, then he came on this thing "My religion is xxx what is yours?"
First I ignored him but he asked me again so I answered "Buddhist." He didn't really understand me and was pretending like he did. So if someone asks me this question in the future what should I say?
Determine what you will say based on what you can learn from the other person with whom you are talking. Listen carefully to what they say and presume nothing about what they mean. Ask careful questions about what a religion is and see whether what you are part of is a religion by this meaning. You may discover that while Buddhism is a religion the Dharma is something greater and more heartening.

The opportunity for sharing of the Dharma includes as much a listening attitude as it does an attempt to explain what we understand and know. Often meeting people on level ground is as much of an assist to others to find their way as comparing views or values may support our own.

When someone asks a personal question, this is an invitation from them (for whatever reason) to get to know us better, to bring our mind to front and show them who we are. Unless they are already our spiritual guide or filial teacher then we owe them no compliance or explanation in any final sense. Our answer can be "I do not know." and this may become an embrace of humility from which we will persistently benefit.

These categories are not rooted and cemented for all time. What is a religion? Is Buddhism one? Is that what it has always been called? By whom? Perhaps the orthodox guy was bold and yet helpful, and his secret instruction to those he was asking was to cause us to wonder whether religion is valuable and how it helps us to come to a wakeful mind. Are 'isms' generally good at doing this?