If you are using {} or [] to fetch multiple documents, you can use '#' followed by a number in the <file> specifier. That variable will be replaced with the current string for the URL being fetched. Like in:
curl http://{one,two}.site.com -o "file_#1.txt"
or use several variables like:
curl http://{site,host}.host[1-5].com -o "#1_#2"