Learn English – the symbol for an “Answer”, if so why we’re not using that

It looks as if Person B is saying that he might go shopping, but that he is not certain. It is common in very informal communication to append a question mark to indicate uncertainty. In speech, this would usually be inflected as a question.

You are not asking a question. You are making a statement that someone should notify you. Your statement is similar to a question in that it expresses your need to know when you can come for the same. You also have your subject and verb transposed.

Let me know when I can come for the same.

is in some ways no different from

Take the dog for a walk.

The first tells your audience to do something - share information with you. The second tells your audience to do something - walk the dog.

A question is interrogative. It requests an answer. Let me know when I can come for the same, does not request an answer. Your audience may often respond to statements by saying, OK, which merely acknowledges they hear you but has nothing to do with when you can come for the same. People may also respond to statements by saying, No. That, however, does not make your statement a question. It merely means your audience heard your demand and is letting you know they will not being doing what you expect.

Your statement as a question is -

When can I come for the same?

Now your audience has been prompted to provide that answer. If you know, however, that your audience does not currently know when you can come for the same, asking, When can I come for the same, is pointless and confusing.

So what you are saying in your statement is that you suspect your audience does not know when you can come but when they do determine when you can come, they should let you know. It can be thought of as asking a question today with the expectation of an answer in the future. Even though your statement is NOT a question and should not contain a question mark, it will be understood as a question.