I import a track, name it "Anything" and then delete it. If the track is re-imported, it is automatically named "Anything 001." If I try to rename it "Anything," Basecamp tells me The track name already exists. Please try another name. It will do the same with waypoints. It seems that Basecamp is caching these names with no way to clear the cache. Anyone have a workaround?
I'm a PC user, but I believe the following is valid for both versions: it's possible it's the way you "deleted" it. In BC, there is "remove from <listname>" and there is "delete". I'm not a Mac user, check your menu that contains these commands when you have an item selected, it may show the key shortcuts. On a PC, the first is the "delete" key, so it can be confusing. The first does not competely delete an item, only the second does. Check your "My Collection" folder or the "Unlisted Data" folder to see if the original "Anything" is still in the database. If you successfully completely delete an item, you should be able to immediately re-use the name.
C14 has given good advice. The specific Mac action is to either right click or control-click on the track name and drag down in the choices to Delete from My Collection.