Norwich-based Redwell Brewing, which employs eight people, has been told customers could confuse the two brands because both brand names begin with "Red" and end "ll".
Redwell was issued with the warning in a letter from Red Bull's brand enforcement manager and has been told it will face legal action if a resolution is not found by the end of the month.
The letter, sent about a month after the first Redwell beers hit the market in April, read: "The term 'well' is merely descriptive and therefore of no distinctive character at all.
"Furthermore the term 'bull' and the term 'well' share the same ending and just differ in two letters.
"The ending 'll' is identical and therefore the terms Red Bull and Redwell are confusingly similar from a visual as well from a phonetical point of view.
"The consumer will thus be confused as to the origin of the services."
The brewery, founded in October, is named after the city's Redwell Street.
Mr Fisher said: "The letter came as a huge shock and a worry. We barely had time to catch our breath before a second letter came demanding an immediate response.
"It seems they have trademarked 'red' but we're not really even using the word 'red'.
"It didn't in a million years occur to us that we were treading on their toes.
"It just seemed like a great name as it connects to where we are based, looks good on the bottle and trips off the tongue.
"Our solicitors think we've got a good case but we haven't got the same financial muscle so we're hoping and praying we aren't forced to change our name."
The friends hired an expert brewer from Sweden to help set up the business and produce two ales and a lager.
They supply pubs in London, East Anglia, Manchester, Newcastle, Glasgow and Edinburgh.
"It was a a dream that grew and grew but this has just hit us for six and the whole thing feels like it is tainted by what's happened," Mr Fisher said.
Red Bull said it would not comment on a pending case.