A double I?
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Fig. 1 - Drawing and transcription of a graffito from Pompeii - Wikimedia Commons
And what about II? The reduplication of the letter I in the middle of a word or name strikes as odd. Leemans assumes that it stands for an E. Two vertical lines are a common variant of the letter E in cursive script, as we can see in many graffiti from Pompeii (fig. 1). In inscriptions, however, this is not a usual way of writing the letter. Another argument for dismissing the reading of E is that the last letter of the inscription (in the third line) has a 'normal' E. Would the mason have used two quite different letter variants on the same stone?
On the other hand, the stonemason might have been illiterate in Latin. He would have then carefully copied the letters from a paper that was handed to him by the customer. That might explain that a cursive variant of the E was copied to stone.
Another solution put forward by Leemans is that the second I was actually a badly executed P.