No, Zhang Ziyi doesn't have an English name. But at the insistance of her agents, she did reverse the order of her name (placing the surname last) when credited in Western films and media. I hear she at least initially regretted the decision. I didn't like it (and still don't) because I thought the Western media should conform to her and her culture, not the other way around.
Now, I wouldn't doubt seeing this happening more often in the future, particularly among new Chinese actors coming to work in the US (except those with given English names, like in HK). Rather than using 'adopted' English names, we'll see them changing the orientation of their given Chinese names.
For example, indications are that Liu Ye (while having no English name) will very likely be credited as Ye Liu in the upcoming film 'Dark Matter' (at least in much of the West).