As far as I can tell, text-overflow is pretty well supported:

http://www.w3schools.com/cssref/css3_pr_text-overflow.asp
https://developer.mozilla.org/en-US/docs/Web/CSS/text-overflow

It was vendor prefixed in IE6.  If it's not available, the name will be shown, truncated without ellipsis due to the overflow:hidden that's also specified on the .message .left .name class, but I wouldn't expect that fallback to come into play in any browser that can actually run jabbr.