Akira Toriyama always based each of his character name with pun intended. Since the Saiyan is originated from Planet Vegeta (Vegetable) then they're more likely to have the name based on vegetables.

Here you can find name puns on many of the characters from the Dragonball, Z, GT series. Some puns are rather obvious, but we put them in anyways.

Theme - Vegetables:
» Bardock = Dock (A Root Veggie)
» Broly = Broccoli
» Kakarot = Carrot
» Nappa = Type of Cabbage
» Panbukin = Pumpkin
» Paragus = Asparagus
» Raditz = Radish
» Seripa = Parsley
» Turles = Turnip
» Toma = Tomato
» Totepo = Potato
» Vegeta = Vegetable

Theme - Fruits:
» Appule = Apple
» Blue Berry = Blue Berry
» Dodoria = Chinese Gooseberry
» Kiwi = Kiwi
» Rasberry = Rasberry
» Tuffle = Fruit
» Zarbon = Pomelo

Theme - Foods & Drinks:
» Chiaotzu = Dumpling
» Chi-Chi = Breast
» Pilaf = Sauteed, Seasoned Rice
» Gohan = Rice
» Krillin = Chestnut
» Launch = Lunch
» Marron = French Chestnut
» Oolong = Type of Tea
» Pan = Bread
» Puar = Chinese Tea
» Shu & Mai = (When Combined) is a Dim Sum Dish
» Tienshinhan = Fried Rice
» Yamcha = Dim Sum

Theme - Dairy Products:
» Burter = Butter
» Ginyu = Milk
» Guldo = Yogurt
» Jeise = Cheese
» Ricoome = Cream

Theme - Instruments:
» Drum = A Drum
» Piano = A Piano
» Piccolo = A Type of Flute
» Cymbal = A Cymbal (part of drums kit)
» Tambourine = A Tambourine

Spoiler:

Theme - Other:
» Buu = Bibidi, Babidi, Buu
» Cargo = Escargo
» Cell = A Cell
» Cooler = Cooler
» Dende - Snail (If an N is added to the End)
» Frieza = Freezer or Freezing
» Goku = Sky or Emptiness
» Goten = Air, Heaven
» Jackie Chun = Jackie Chan
» Kai = God
» King Kold = Cold
» Mr. Satan = Satan
» Nail = A Nail
» Shenron = Dragon God
» Slug = A Slug
» Videl = Devil (Scrambled)

I think Broly: Broccoli is a stretch.

Breast is a food or drink? 0.o

Broly is Broccoli u noob

Oh now I see it...