Here's a
reminiscence article from Frank Anzalone about the opening day ceremony. The publicity materials there said just Indiana Jones Adventure.
Here's the
alphabet decoder card they gave out in 1995 which just says Indiana Jones Adventure.
The
attraction poster.
Here's the
original sign.
That, so far as I know is still the sign, but without the AT&T sponsorship.
Most of the early promotional material I can find pictures of just say Indiana Jones Adventure (and the current Disney materials label it as such) I don't doubt they promoted "The Temple of the Forbidden Eye" but I wonder if it was officially part of the name or more of a subtitle.
But if it was then the official unwieldy name was Indiana Jones Adventure: The Temple of the Forbidden Eye.
(Somewhat strangely, Dave Smith lists it as
Indiana Jones Adventure; Temple of the Forbidden Eye in
Disney A-Z.)
Regardless, I'm pretty sure the official name
now, which is what we're talking about, is just Indiana Jones Adventure. The full name is used for everything else on the attractions page at the Disneyland Web site and this is how it is listed there. Same with official Disneyland press releases which also tend to be overly formal in referring to rides (probably because of lawyers).