Your identity may be intangible, but you can certainly be deprived of its proper use by someone successfully impersonating you. So unlike digital piracy (for want of a better term) something is taken from you in a manner that precludes your own use of it.

More to the point though, labelling the act of downloading the latest film as theft is not conductive to a discussion about the moral justification of piracy, because you are using loaded language to condemn it even before presenting an argument. That is, there appears to be no strong consensus that piracy falls under what is commonly referred to as theft.

(I am under the impression that the term digital piracy did stick regardless of one's position in that debate.)