Not usually. Do you have more context?

No, it can't. If you sign your name, this is known as a signature. As a noun, 'sign' can be something concrete, such as a 'Stop' or 'Turn left' sign on a road, or a 'Do not enter' sign on a door. A sign can also be less concrete. For example, when birds start to build their nests, this is a sign that spring is coming.

Your question was a little different in the message that you sent me. In this case, "signature" would just be how you write your name. Your "sign" would be a picture or symbol that represents yourself. Hand gestures can also be used as a sign.

Do you mean, when someone asks you to 'sign the paper?' or someone says, "Please sign here." Then, yes they are asking for your signature. But, as others have mentioned when you say 'someone's sign,' it means something different.

If you are writing a dialogue for Star Wars or Harry Potter or James Bond it could be something like: A: How would I know it's him, Mother? B: When he arrives, he will give a sign. A sign of the Cross. If so, you give him a glass of Glenlivet on the rocks, whereupon he would say, "Have you got my kilt?" You should then say, "Her Majesty the Queen Mother is dead." If he responds, "Long live the Pope", give him the emerald. If he misses any of that, or his sign is not a sign of the cross, just take him to table 9 in the restaurant.