It seems that although both the Hungarian and the English words share the same Ancient Greek root, the Hungarian word (herma) has an additional semantic meaning not found in English. According to the Merriam-Webster dictionary, a herm is "a statue in the form of a square stone pillar surmounted by a bust or head especially of Hermes".

Several articles point out that a reliquary (an object used to store relics) may have several forms, such as a philatory or a monstrance, depending on their intended use. However, no special words refer to the actual body part encased in them. Articles simply call them "an arm reliquary" or "a foot reliquary". To denote the object that encases a head/skull fragment, one should rather write "a head reliquary".

The description of an object from the British Museum:
"Head reliquary of St Eustace and wooden core; silver-gilt repoussé head with gem-set filigree circlet binding straight hair; nine gems composed of varieties of quartz (rock crystal, chalcedony, amethyst, carnelian), two of aragonite (pearl, mother of pearl), one of obsidian and six of glass."

An altar combined with a reliquary is called a reliquary altar, hence my suggestion to write an "altar with head reliquary".