Reed employment agency is offering schools support to become specialist colleges on the condition that they print the phrase "A Reed college" underneath their names on letterheads and other materials featuring the school name. The company is also requesting that the schools it helps use a dolphin logo.
The Specialist Schools Trust said it believed this was the first time a company had made such a request.
Professor Alec Reed, founder of the agency, has set aside pound;500,000 which he is offering to schools to help with their bids to gain specialist technology or business and enterprise status.
A Reed spokesman said the company was not asking schools to change their names, merely to add the words "A Reed college of enterprise" as a strap-line.
The name and logo were part of a drive to make all Reed-sponsored schools appear like a uniform "brand" - several schools had already agreed to use them, he said.
"The dolphin symbolises enterprise, it suggests leadership and intelligence," he said. "It is part of the branding for the 12 or more schools which Reed will sponsor. Schools which become sports colleges have their own logo so it should be the same with our enterprise colleges."
Staff at a secondary school which contacted The TES said they had been interested in the sponsorship offer but had changed their minds when they heard about the conditions. Their view was that incorporating the Reed made a big difference.
One senior teacher said: "The document Reed sent us said the school name had to be "associated with Reed". Our staff felt that this was just going too far, a price too high to pay. We are talking about a total change of identity which is not acceptable."
Schools that join the Reed "brand" will be encouraged to meet and collaborate on teaching enterprise.
The National Union of Teachers said that Reed's offer was yet another example of the growing commercialisation of schools.
John Bangs, NUT head of education, said: "The problem is the Government is trying to convince people that businesses want to support schools purely out of altruism."
Professor Reed has already given pound;2 million to an city academy in Ealing, the West London academy, which specialises in enterprise.
Professor Reed said: "In the 21st century enterprise is going to be at the heart of our success as a nation, and I want to do all I can to stimulate its study.
"Our quality of life, in all its aspects, will be made better if we are an enterprising people."
The Department for Education and Skills said it did not wish to comment on the proposals because discussions between Reed and the Specialist Schools Trust over final details were ongoing.
Specialist schools are offered the use of a logo for their specialism, such as modern languages and sports, but none of these logos are linked to a specific business sponsor.