A Signature need not be a name, much less the signer's name
A signature can be any word or mark which represents a person, and which indicates that the signer has read and agreed to the document. It need not be the person's name, nor written using the standard "roman" alphabet used for the English Language. Nor is there any ...
No for the U.S.
There is no criteria for graphic complexity in the United States. A signature can still be the historical "X". If it is some representation of your name, as it ordinarily is, it not need to be remotely legible or a representation of your full name.
Usually, a signature is simply someone's name written in a stylized ...
In the US, your "signature" is presumed to be your full name written in your own handwriting (in cursive). It may be OK for it to be written in a language other than English, but expect it to raise eyebrows if it is.