When a bill is first introduced in the House or Senate, it is assigned a number and its text includes a "short title," i.e., the law's popular name. Though this name may change, the bill number stays with the legislation throughout the process. If a bill becomes law, it gets a public law (Pub. L.) number in its first printing as a slip law. All the slip laws are then printed chronologically as session laws in the Statutes at Large (Stat.), before being broken up and codified by subject in the U.S.C. (For more information, see this guide's Pub. L./Stat. tab.)
When looking for a compiled legislative history, using only a law's popular name to find one may be sufficient. If looking for a list of citations, you generally need to know the Pub. L. or Stat. citations. Whatever the case, taking the time to find the original enacted bill's number is a good idea, if only to make better sense of the legislative history documents themselves.
One way to find a law's original bill number is to look up its Pub. L. or Stat. citation. Whichever citation you use, the statute (since 1904) will display the enacted bill number at the top. (For laws prior to 1904, see the Legislative Reference Checklist by Eugene Nabors: Print and Online.)
Another way to find the bill number is to use ProQuest Legislative Insight's "Citation Checker" feature, in which you can enter any citation (Pub. L., Stat., or bill) you have to find the other two.