What would an asteroid inside of Mercury's orbit be called? The first Vatira asteroid has been discovered. This makes me wonder if there is already a name for the hypothetical class of asteroids that orbit entirely inside of Mercury's orbit. It wouldn't be the first time that an astronomical class is named before being actually observed.

Is there a name to designate the hypothetical subclass of Atira asteroids whose aphelion is closer to the Sun than Mercury's perihelion ?
The name used for such objects is vulcanoids. This term refers to the hypothetical intra-Mercurian planet Vulcan, which was proposed by Urbain Le Verrier (best known for his successful prediction of the existence of Neptune) to account for the anomalous precession of Mercury's orbit that is now explained by general relativity.
Note that the expected number of vulcanoids is low: the Yarkovsky effect should  clear out objects smaller than 1 km on ~gigayear timescales (Vokrouhlický et al., 2000), while the YORP effect would be effective at destroying larger objects by spinning them up until they break apart (Collins, 2020). Observational constraints from NASA's STEREO mission suggest the number of objects larger than 1 km may be no more than 76 (Steffl et al., 2013).