Arab tribes where known by lineage through their fathers to their tribes, hence they did not have first name and surname as we would understand here.
Muhammad, father was called Abdullah, who are part of the Hashim clan from the greater Qureshi tribe.
The name means one who is most praised, it was a name that was given to him by his grandfather who when asked why he gave him that name as it was uncommon, said, "I hope that he will be praised in heaven and on the earth."