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The Children's Trust, based in Tadworth, Surrey, is in dispute with officials over plans to use the name for co-ordinated health, education and social care services.
The charity is concerned that use of the name will cause confusion about its work and the government-backed sevices.
The Trust provides specialist care and education for severely disabled youngsters, many with complex health problems.
Formerly the rural branch of Great Ormond Street, the trust was set up as a charity in 1983, and took its new name 10 years later.
A spokeswoman for the charity said of the Government's plans: "We welcome any initiative that improves services for children."
But its members are angry that the DfES wants to use its name.
The spokeswoman added: "We are currently in discussion with the Government about the use of the name Children's Trusts.
"We very much hope that these discussions will lead to a mutually acceptable resolution."
A DfES spokeswoman said: "This charity is disputing our use of the term. We have met them to seek a solution and will continue to work with them until we do."
She added that the Government had not considered any other names for its services, should no agreement be reached.