John (Yahya) is also mentioned 5 times in the Quran. He would be the next answer on the quiz.
But then if you look at the hadith Muhammad is mentioned ad nauseum. The hadith are considerably more substantial than the text of the Koran.
On the other hand, if you look to the hadith and sunnah, which are many many times more voluminous than the Quran, then Muhammad is mentioned there infinitely. The hadith were recorded by Muhammad's followers who recorded virtually everything he ever said or did. But they are not verses of the Quran which were the messages Muhammad claimed to be transmitting from the divine and having his followers commit to memory.
And We have sent thee not but as a mercy for all peoples.
Verily you have in the Prophet of Allah an excellent model, for him who fears Allah and the Last Day and who remembers Allah much.
And as a Summoner unto Allah by his command, and as a Lamp that gives bright light.
And thou dost, surely, possess sublime moral excellences.
So... yeah. He mentions himself quite a lot.. but rarely uses his own name. Like monarch who refer to themselves in the "royal we."