At the risk of sounding like a broken record, if you do a forum search for either topic, you'll find a lot of prior discussions about both issues.
Afz sums it up nicely. Consider travelling to somewhere like South Africa: Due to a very high crime rate, it's constantly a medium-risk destination to visit. Lebanon is completely different. The risk profile there is quite lumpy - it's either very safe, or very dangerous, depending on circumstances. Everything was fine there in June 2006 and April 2008, but wars broke out in July 2006 and May 2008 with practically no warning whatsoever.
At the moment, Lebanon is fine, but tensions are building due to the Hariri Tribunal and the threat of war between Israel and Iran, which, if it happens, will almost certainly end up dragging in Lebanon.
Just keep that in mind when you're planning - if you're concerned about safety, it might be best to make sure that you fly in and out of Jordan or Syria - that way, you can lop off the Lebanon part of your trip quite easily if problems break out.
As for a Jewish surname, it shouldn't cause any problems at all. If you search the forums, you'll find a few reports from openly Jewish people who have travelled to the region and not experienced any problems. Although if you discuss the Israel/Arab conflict with anyone, you'll be likely to hear views that would be labelled as anti-Semitic in the west, almost all Levantines - even Assad and militant groups like Hezbollah - do take pains to point out that they have no problem with Jewish people, but that it's Zionism and the Israeli state that they have a problem with. For a pretty clear example of this, check out the rebuilding/restoration of the main synagogue in Beirut.