When reading "The Secret of Hittites" I would always laugh when Suppiluliuma was mentioned, his name sounds like what you would call a fat bunny, or I don't know, it's just hard to take seriously.
Now I wonder if the Hittites would think the same, because all their other kings had names that sound unusual to me but that I can respect, like Hatusil, Mursil, or Labarna.
So, what did hittites think of that name?
Suppiluliuma has a perfectly good Anatolian etymology (šuppi, "pure, holy" + luli, "lake, spring, well"), as do the other royal names like Hattušili (Hattuša + -ili, "Man of Hattusa") and T/Labarna (Luwian tapariya, "to be powerful, to rule"). There is no reason to suppose that it would have sounded strange to the Hittites.
In any case, all surviving Hittite texts come from official contexts, particularly the royal and temple archives of Hattusa. Official texts certainly won't record what the king's subjects thought of his name!