During the 2nd to 3rd century, Romans would wear a pendant which we call a Hercules' Club, in much the same way a modern Christian would wear a crucifix. https://en.wikipedia.org/wiki/Hercules%27_Club_(amulet) What would the Latin term for this pendant be? If there is an ancient Greek term for this pendant, I would be interested in learning that too. Would the term for the pendant be different from the term used to show Hercules' ownership of a club?
I'm not sure we have direct evidence of this particular pendant, but we do have what the Romans called the club and what they called pendants in general.
The club is called the clava. Varro (LL 8.26.6) mentions it when he's discussing Greek nouns in Latin:
utrum Herculi an Herculis clavam dici oporteat
whether we ought to say club of Herculus or club of Hercules
Tacitus also mentions that the Aestii wear a pendant of a boar to honor the Mother of the Gods.
Matrem deum venerantur. Insigne superstitionis formas aprorum gestant
The worship the Mother of the Gods. They wear the forms of boars as an emblem of this cult.
The pendant itself could be called different things, just as in English we could also say "amulet." But given Tacitus' language, it'd probably be simplest to say insigne clavae Herculis or formam clavae Herculis.
To add the Greek: the usual word for a club, including specifically Hercules' club, is ῥόπαλον rhópalon.
There are various words for a pendant or amulet, including περίαμμα períamma and περίαπτον períapton, both meaning "(something) hung around". So a "a pendant of Hercules' club" could be something like περίαμμα Ἡρακλέους ῥοπάλου períamma Hērakléous rhopálou, though I don't know whether that particular phrase is attested anywhere.
We have a few references to what the Romans called Hercules’ original club. For instance, [line 625 of Seneca’s Hercules Furens says,
agnosco toros umerosque et alto nobilem trunco manum.
Frank Justus Miller translates this as:
Aye, now I recognize the bulging thews, the shoulders, the hand famed for its huge club.
Where trunco is the word translated club.
On line 466 of the same work, his club is called a clava.
In the Aeneid, we have at Verg. A. 8.219
Hic vero Alcidae furiis exarserat atro
felle dolor: rapit arma manu nodisque gravatum
robur et aerii cursu petit ardua montis.
Black bile burned hot in Hercules; he grabbed His weapons, his great knotted club, went rushing Up to the mountain-top.
This translates robur, literally hardwood or oak, as club, and gravatum, literally heavy, as great. Another translation makes nodisque gravatum robur into “his club of knotted oak,” implicitly translating gravatum as club and robur as of oak.