The application to register her name was made by the Roslin Institute after Zanussi, the electrical manufacturers, produced an advertisement showing a sheep called Dolly with the caption "The Misappliance of Science".
Dr Harry Griffin, assistant director at the Edinburgh institute where Dolly was cloned, said the advertisement was derogatory and had incensed scientists.
"It is grossly untrue to suggest as a statement of fact that Dolly is a misappliance of science," he said. The science that led to Dolly, he added, would have very large positive benefits for society, particularly in medicine.
"Our technology has already been used to create sheep that will produce human blood clotting factor in their milk so as to provide new treatments for haemophilia.
"In the future, we expect that the same technology will help solve the chronic shortfall in organs for transplant." He said that Zanussi was "clearly ignorant" of the reasons behind the cloning.
The company said it had agreed to withdraw the posters "as a goodwill gesture".
A spokeswoman for Zanussi said the poster was part of a pounds 3.5m campaign that was due to run until November.
It showed three different images with the statement "The Misappliance of Science". The first was a nuclear mushroom cloud, the second a dead fish in a polluted river, and the third was a sheep called Dolly, but it was not the cloned animal.
John Kershaw, head of marketing at Zanussi, said the advertisement was meant to provoke debate.
"The application of science has revolutionised the 20th century and brought enormous strides forward in areas like medicine. But we feel it is still important to evaluate the role science should have in everyday life and in the future," he said. "Our advertising is aimed to develop discussion. However, we have decided to withdraw this particular poster in response to concerns expressed by the Roslin Institute because we do not wish to offend them."
But Dr Griffin said the institute did not want to take any more chances that companies would misuse Dolly's picture. "We hope that by trade marking Dolly we will have a mechanism that will prevent inappropriate use of her," he said. "The Scottish National Party used her on posters to suggest that the opposition parties were all clones. That was fine because it was not denigrating our science but once she is a registered trademark then people will have to ask us if they can use her picture."
He denied that the institute had taken the action to keep any potential merchandising power for itself. "We discussed [Dolly mugs and T-shirts]," said Dr Griffin. "But it was decided that it would be inappropriate."