Do you mean the identity of the person? No. In order to do that you would need to use a third-party signing authority that validates the identity of the person and then issues them with a signature profile.
Thanks for using Adobe Acrobat DC. If you want to get the identity of the user then no, we don't have this functionality in Fill & Sign as of now. But we would really like to know about the usecase with which you want to use this information.