I was amazed someone would know my name.
(source)In that situation, can would be used?
Answer
Yes, although it’s a matter of context more than anything. Just taking the sentence by itself, it’s better to have:
I was amazed that someone would know my name.
If you can give more context, I can provide a better answer for you.
Attribution
Source : Link , Question Author : Listenever , Answer Author : Dave Moore