What should I call you? This is almost never used in common conversation. This would only be used if there are multiple acceptable names but you are asking which name to use. For example, you meet a man and he says "My name is Michael but people call me Gordo" then you ask "What should I call you?". I more formal way is to ask "What name do you prefer?" What can I call you? This is also almost never used in common conversation. Literal translation is "What name am I able to call you?". I think it's used more in a state of pondering. For example, you're trying to think of a name for a cat and as you think to yourself, you say "hmmmm what can i call you? ***thinking*** ***thinking*** What can i call you?". How can I call you? This is asking the best way to call someone. For example, you're in a foreign country in the middle of a small town that has no phones. So you ask your friend "How can I call you?" ...and his reply will be something like "The only hotel with a phone is La Rosa Inn".