Danny Lucas, 49, from Wrotham, Kent, launched the app last year in an effort to raise awareness and discourage litterers.
LitterGram asks users to photograph, share and geo-tag litter they see on the streets.
But Facebook, which owns the photo-sharing service Instagram, argues that the use of “gram” in the title could undermine its brand.
The tech giant also contends that the use of photography and social aspects of the app are too similar to that of Instagram.
Lucas said he has been given until Friday to confirm plans to change the name from LitterGram.
He had hoped the app would prove to be a revolution in combating Britain’s litter problem.
Lucas has previously publicly appealed to Facebook founder Mark Zuckerberg asking him to relent and claiming the “unreasonable demand to rebrand will kill our momentum at a time when support is building among councils and others”.
Facebook has described the motivation behind LitterGram as “admirable” and said no steps had been taken to file a lawsuit against LitterGram, but that it had an obligation to take reasonable measures to protect its brand.
Lucas has disputed claims he was planning to trademark the LitterGram app, saying that he had instead reached a compromise with Facebook to trademark bags, T-shirts, posters and other merchandise.
He said: “We are saying, ‘Don’t stand on us, support us’. We have got a name that’s now known, some 4,000 primary schools have been sent our education animation. No-one is going to know us if we change our name.”
Facebook has said it hopes to reach an agreement with Mr Lucas without going to court.