Most Dragon Ball fans are fairly certain they know the origin of Gohan's name. One might think that he was named after Goku's Grandpa Gohan. However, it's not quite as simple as that.
Contrary to popular belief, Gohan was not named after his great-grandfather. At least, this isn't the case in the anime. Akira Toriyama more than likely thought of Grandpa Gohan when he gave Gohan his name, but the anime provides a slightly different explanation for this.
Where Did Gohan's Name Come From?
The origin of Gohan's name was given in Dragon Ball Z Episode 171, "Memories of Gohan." As the name of the episode suggests, Chi-Chi had a flashback to when Gohan was still an unnamed baby. At the time, nobody was sure what to call him.
The trio of Goku, Chi-Chi, and Ox-King all worked together to come up with a name for the newborn baby. Chi-Chi, wanting the boy to become a scholar, tried calling him either Einstein or Archimedes, but the boy cried at both of these names. Next, Ox-King came forth with a long list of ox-based names; the boy cried at these suggestions, too. Goku could only think of how hungry he was.
As Chi-Chi was berating Goku, a certain set of phrases popped up. She told Goku that he had just eaten "breakfast" and asked for him to wait until "lunch;" in Japanese, these words are pronounced asagohan (朝ごはん) and hirugohan (昼ご飯), respectively. Both of these phrases seemed to make the boy laugh. Ox-King stopped Chi-Chi to confirm this; he also confirmed that the baby would laugh at the simple word gohan (ご飯, lit. "cooked rice"). Goku looked at the nearby Four-Star Dragon Ball, took all this as a sign, and dubbed his child Son Gohan.
The misconception about the name's in-universe origin likely comes from the English dub of Episode 171. In this version, Chi-Chi still scolded Goku, but instead of talking about breakfast or lunch, she asked him whether [Grandpa] Gohan ever taught him manners; the end result was the same as before. This change to the dialogue was probably done to make up for the lack of the phrases asagohan and hirugohan in the English lexicon. In fairness, however, the kanji reading for Son Gohan's name (孫悟飯) is the same as Grandpa Gohan's.
Whatever explanation there is for Son Gohan's name out of universe, this is the in-universe reason he has it. It makes for a charming little anecdote that shows fans a part of Dragon Ball's history that they couldn't have gotten in the canon manga. It's a little contradictory to how one might expect Gohan to get his name, but there's just enough of the presumed truth behind it to make it believable.