Oatly, the plant milk maker backed by Oprah Winfrey, is in a court battle with a Cambridgeshire farm over alleged trademark infringement.
Lawyers for Oatly sought a High Court injunction on Thursday to stop Glebe Farm Foods selling its PureOaty brand.
Oatly said it contacted the PureOaty makers in early 2020 saying "their branding infringed our trademark".
Farmer Phillip Rayner, who owns Glebe Farm, said the PureOaty name was "a nod to the purity of the product".
Mr Rayner said that his company began producing the beverage using British-farmed oats about 18 months ago, but Oatly now wants Glebe Farm to stop using the PureOaty brand and change its packaging.
The Cambridgeshire farmer said: "Oatly says the name and packaging is too similar to theirs, but when we compare the two products side by side, we are surprised by this."
A spokesperson for Oatly said that since the 2020 letter, "we unfortunately received no constructive response from them. We are therefore now involved in an ongoing court case and we have no further comment as we await the results."
The case at the London High Court is expected to conclude on Thursday.
Oatly, which was founded in the 1990s and produces a milk substitute made from oats, has grown rapidly in recent years.
Its oat milk is now sold in 60,000 shops and more than 32,000 coffee shops across 20 countries and the company is now worth more than $15bn
Other celebrity investors in the firm alongside Ms Winfrey include Jay-Z and Natalie Portman, It has also had investment from the state-owned China Resources and Verlinvest, a Belgium-based investment firm.