Can you put the Targeting Computer card on the Elite HK Assassin Droid?

It already has an ability named that, but I don't know if attachments counted as the abilities themselves, even if they have the same name.

And if you can put it on it, then it allows you to use both abilities right? But only on different dice, as I know you can only reroll a die once.

Yes you can, just like you can attach Combat Suit to the elite Echo Base Troopers.

Even when the name of the abilities are the same, they are two separate sources of the ability, so you can then reroll two dice for each attack.