Amalar wrote a letter "To his dearest father and most acute rhetorician, the prophet Jeremiah in our Jerusalem." The reference to Jerusalem threw me because at first, I was looking for a ninth-Jeremiah in Jerusalem, unsuccessfully. Eric Knibbs' notes on the text at the back of the volume identify this person as "Archbishop Jeremy of Sens (818–827)."
Amalar writes (Knibbs' translation, pp. 267–269):
Our countrymen write the name of our savior Jesus with the letter "H," and I am puzzled about the reason. I know that, if there is a reason that an "H" in Jesus's name is placed after the "I," it is not unknown to you. If you know, tell your son. If you do know, I am certain that it will be in the storeroom of your mind to pass the reason on to me. ... Now the Greeks write that name with the letters "I" and "C," and they read "Isus." Thus it seems to me—if it does not seem otherwise to you—that what we read as "Iesus" should be written with an "I" and an "H" and a "C" or an "S." I ask that you tell me with which letters I should write the stated name.
Jeremy of Sens responded and explained to Amalar that the letter was [and I am using lower-case here for clarity] not actually 'h' but 'η,' though they are written the same.
To be honest, I have wondered this too—why do we see IHS in the Latin tradition, which we still see today? I remember as a kid somebody in my rural southern church culture explained to me that he thought it meant "In His Service." I guess Jeremy's answer still doesn't really explain why we see the Greek eta in the Latin tradition, only that the 'H' is an eta. Has anyone come across any patristic/medieval discussions of why the Greek eta was used? If any of you, our readers, does know, I am certain that it will be in the storeroom of your mind to pass the reason on to me.