Actually, Clint gave him that name during the filming. Lee Van Cleef said it in an interview.
"That name `Angel Eyes' in The Good, the Bad, and the Ugly; was that tailor-made specifically for you?" I asked.
"If it was in the script, I didn't see it," Van Cleef recalled, "and I'm usually pretty careful about giving scripts a close reading. I think Clint came out with it one day. It just kind of sprung out, and it was used ever since. I made no complaints about it. They've referred to me as that quite often in publicity since that time. I thought it was pretty good."
The full interview can be found here:
http://members.aol.com/ilcattivo2/bijou.htm*Note* This is not my site.