What is the name of the dog of people of the cave (Ashab al-Kahf)?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is no mentioning in the Quran or the Sunnah of the name of the dog of the people of the cave. We cannot know the name of this dog if it is not mentioned in the Quran or the Sunnah because it is not something that can be deduced by reasoning.
Know, dear brother, that knowledge such as this matter is not important, and we do not need it and its ignorance does not cause us any harm. The Muslim should occupy himself in learning what is mandatory, what is forbidden, what is blameworthy and what is likable as this knowledge results in doing that which is rewarded and avoiding that which is prohibited.
Abu Hurayrah narrated that the Prophet said: “Devote yourself to that which benefits you and ask help from Allah and do not fall short (of doing that).” [Muslim]

Allah knows best.