$url =~ /.+\/(.+)/;
$image_name = $1;
[download]

This will make use of the fact that regexes tend to be greedy, and match as much as possible. In the above, the . means anything but a newline, the + means one or more of them, and the \/ means a slash. The \ is needed in front of the slash to "escape" it, so it isn't interpreted as the second delimiter of the regex. So the regex up to that point will match everything up to the last slash. Then the parentheses around the .+ (one or more of anything again), will store what the .+ matches in the $1 variable. Then the next line puts that in $image_name.

If you wanted to be sure to only match on a JPEG, you could use (.+\.jpg) for the part in parentheses instead.

You really should check out perlrequick, perlretut, and perlre to learn more about regexes, because I left out a lot in my above explanation. They're not that hard to learn most of the basics, and a lot of fun I think.