You could use wire but it would have a very different look: http://www.google.ca/#hl=en&cp=11&gs_id=1x&xhr=t&q=wire+name+necklace&pf=p&sclient=psy-ab&site=&source=hp&pbx=1&oq=wire+name+n&aq=0&aqi=g2g-v2&aql=&gs_sm=&gs_upl=&bav=on.2,or.r_gc.r_pw.,cf.osb&fp=47ae9ca12abe4e3f&biw=1280&bih=680
For those you can use pliers to bend the wire into the shape of the name - theres lots of tutorials online for those! I think they look pretty too!
But for a necklace to look like the one in your picture you're not going to want to use wire. This one looks like it was probably machined. To make it by hand you would need to get sheet metal and cut the shape out with a jeweler's saw. Alternatively you could try using a laser cutter service to cut the metal for you. You could also try using precious metal clay (it fires into silver or gold, etc.) but you would need to find a way to fire it. If you're not dead set on using metal perhaps shrinky dink plastic would do the trick for you?
If you don't want to invest in a lot of materials/tools using wire is probably your best bet! or shrink plastic!
as for attaching it to the chain - you can use 2 jump rings.