There are 16 elements in FF7. They are usually stored as a bitmask, but are instead stored as an index in the case of materia.
The battle text (part 26 of the KERNEL.BIN) refers to "Ice" as "Cold" and "Bolt" as "Lightning".
The names of elements 09h - 0Eh are not ever mentioned in the game. However, they are stored as battle text for the purpose of sensing.
"Hidden/Ultima" has no name mentioned in the battle text.
"Hidden/Ultima" is on only a few enemy exclusive attacks including Ultima Weapon's Ultima Beam. Elements 0Ah - 0Eh are considered Physical elements (though not enforced as such) and show up on physical attacks. Non-elemental attacks, such as Bahamuts' Flares, have no elements selected.