“boon” meaning “blessing, benefit” come from Old Norse “bón” where it meant “prayer” or “petition”. This word ultimately comes Proto Indo European *bʰeh₂- where it meant “to say”.
“ban” comes from Proto Germanic *bannaną where it meant “curse” or “forbid” and it too came from Proto Indo European *bʰeh₂-
“fame” comes from Old French “fame” where it meant “celebrity” or “renown”. This word came from Latin fāma where it meant “talk”, “rumour” or “reputation”. This word ultimately also came from Proto Indo European *bʰeh₂-
You may be wondering how “prophet” is related? Well, it came into English from Latin prophēta. But Latin got it from Ancient Greek προφήτης (prophḗtēs) where it meant “one who speak for a god”. The “phḗ” part comes from “phēmí” which means “I say”, and you guessed it, that too comes from Proto Indo European *bʰeh₂-
All of these are examples of semantic shift, which means that words change meaning over time. “boon” now means “benefit”, but it used to mean “prayer” or “petition” which is usually something spoken.
“ban” is also derived from the Proto Indo European word “to speak” because when people were banned it usually was the result of spoken commands, as you can see in the Old English version of the word. “ban” comes from Old English “bannan” where it meant “to summon” or “to proclaim”.
“prophet” is someone who speaks for a god, so the speaking connection is clear there. “fame” is quite interesting because it started out just meaning “reputation” or “rumour”. Well, as people talk about someone, there reputation can grow, and as your reputation grows, you might eventually become famous.
Word connections are all around us, and these are but a few of them