Does copyright protect the title of the lyrics alone?

[Amelia.pd]

If the same piece of public domain music has two different titles and sets of words and only one version of the lyrics is in the public domain can the music be used with the title alone of the non public domain lyrics?

[Carolus]

In the USA, at least, names, titles, and short phrases are not eligible for copyright protection. However, they can be protected as a trademark, which has no term of limitation as long as the trademark is in use.