I have an excellent document I downloaded from the web that lists every Liberty ship and its fate, up through about 1970, at any rate. It's at home, so I will PM you the web address tonight.
As for ship's names - if you are going to model your Liberty as serving during WWII, it wouldn't have a name on the hull once it entered service. This was a security measure. Some Liberty's did have a name board on the railings on each side of the bridge deck, but that was not the usual thing.
At launching, Liberty's would usually have the name in white paint on each side of the bow. Not sure about across the stern. If you want small, custom-printed white decals, give Mark at Starfighter Decals a shout - starfighterdecals@verizon.net . I've used him several times in the past and he is quite reasonable.