It depends on where are the people from you communicating with.
In China mainland, people tend to use "奶酪", "乾酪" and "乳酪". All these 3 words show how Chinese definite it according to its characteristics. It's a example of what we called "意译" (translation according to original meanings or just give a new short definition). "奶酪" is more often to use.
In Taiwan, people tend to use "起士", "起司" and "芝士". All these 3 words are sound similar/close to the original word "cheese". It's a example of what we called "音译" (rough transcription according to pronunciation). And what mainland Chinese say before taking a photo is ”茄子“, which is also a rough phonetic transcription of "cheese". I haven't noticed its etymology until you mentioned it. But I don't know which one is more often to use among these 3 words.
I can't speak for everyone, but it's like a general case. Maybe there are some differences between all these 6 words, yet many people like me just don't know and don't care about the possible differences. BTW, mainland Chinese have a word "牛奶布丁" for "milk pudding".