Wiltshire firm Eat Square started making "square pies" earlier this year.
But the phrase is a registered trademark of London-based Square Pie, which has taken action to protect its intellectual property rights.
Alex Joll, from Eat Square, said: "We have to stop calling them square pies, so from now on they're just pies."
Based in Bradford-on-Avon, Eat Square was set up in 2014 with the idea of offering "square meals" including square pies.
But in July, Mr Joll said it was a "bit of a shock" when he got a letter telling him to "stop using Eat Square, Square Pie or anything to do with square".
"We've taken every reference to square pies off our website - there's pictures of square pies but we don't call them square pies," he said.
"We'll also be finding out next month if we can keep our name Eat Square, but we'll keep making square pies and that's the main thing."
Martin Dewey, the founder of Square Pie in London, said it had no objection to Eat Square making and selling square-shaped pies.
He said the dispute was over the adoption of "branding and associated language" which had various trademarks in place.
"I had no reply from Eat Square when I wrote informally and sadly have had to use legal methods," he said.
"There's more than enough pie lovers to go round, without trying to pass off people's branding and goodwill built up over 15 years of very hard work."
A company which makes square-shaped pies has been told it cannot call them "square" by a rival pie maker.