Lowdownapp - a digital personal assistant - allows users to tell friends they have arrived at a location by pressing the "HERE" button.
A standalone app for checking in to locations, called HERE, has also been released by the firm.
Nokia said the name would confuse the general public into thinking it was part of Nokia's own HERE range.
Nokia's HERE is the Finnish firm's brand name for apps and software relating to mapping and navigation.
The company said it had so far invested $12m (?8m) in promoting the HERE brand.
In a letter seen by the BBC, Nokia gave London-based Lowdownapp a deadline of 10 February 2015 to rebrand the "HERE" function of the apps.
"Our client has invested heavily in building and promoting the HERE brand since launch," the letter from Nokia's lawyers to Lowdown app read.
The firm said it had registered trademarks for the word when it related to computer software, such as apps.'David versus Goliath'
The letter added: "Your use of the HERE sign is likely to deceive members of the relevant public such that they will believe your business is connected with or part of our client's business, when that is not the case.
"This amounts to a misrepresentation that will cause damage to our client's goodwill in the UK and amounts to passing off."
David Senior, chief executive of Lowdownapp, described the threat as a real-life David versus Goliath.Nokia said it had so far invested $12m (?8m) in promoting its HERE brand
"It's ludicrous - people say, 'I'm here,' to announce their arrival, which is why we have it as a service.
"As a small start-up trying to deliver value to users we don't think a multi-billion dollar company will be affected by this.
"Life is hard enough without Goliaths squashing Davids - maybe they should focus on creating a better mapping service than Google or Apple than squishing a minuscule business."
Mr Senior said he would probably remove the HERE standalone app from relevant app stores - but was taking further legal advice on whether to remove the "HERE" button from Lowdownapp.
A spokesman for Nokia could not be reached for further comment.
Follow Dave Lee on Twitter @DaveLeeBBC