names - 孫悟飯 - Songohan, why non-Japanese say it comes from "gohan = meal/cooked rice"?

As a French I've always heard that Songohan's name comes from gohan meaning meal/cooked rice. The English Wiki says the same and even mentions ご飯.

But I don't understand why, since the names in the family are like this:

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  孫悟空 Songokū

  
  


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  孫悟飯 Songohan

  
  


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  孫悟天 Songoten

  
  

So it seems only the last kanji changes between the characters, and since 飯 alone already means meal/cooked rice, and 悟飯 alone doesn't mean anything, why do we focus on gohan and not only han to explain the name of the character?

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EDIT: after reading your answers, I realized my mistake was to read 飯 alone as han. That's why I didn't understand people saying "the name means meal because of go + han" since to me han alone already meant meal.

I'm sure noone understands what I mean but thank you, it's clear now.