A judge in London has ordered Twentieth Century Fox to "cease naming" the series "Glee".
But Deputy High Court judge Roger Wyand said his order would not come into effect until the Court of Appeal had given its backing.
Comic Enterprises claimed that Twentieth Century Fox's broadcast of Glee in the UK breached its trademark rights to the phrase The Glee Club.
Twentieth Century Fox disagreed.
Judge Wyand ruled in favour of Comic Enterprises in the trademark dispute in February.
Twentieth Century Fox said it would appeal against his ruling.
The judge made his order on the use of the name today.
In February, Judge Wyand concluded that Comic Enterprises - which operates Glee Club comedy venues - had established that Twentieth Century Fox had infringed its trademark rights to the words "The Glee Club".
He said Comic Enterprises' trademark was "suffering detriment" and there was a "likelihood of confusion".
But the judge said Comic Enterprises had not established that Twentieth Century Fox had "passed off" Glee as being associated with Glee Club venues.
He said he was not convinced that "such confusion is likely to be said to cause damage" to Comic Enterprises.
Lawyers for Twentieth Century Fox argued that in the wake of those conclusions an order requiring a series name change was unnecessary, unfair and disproportionate.
They said changing the named would be costly and complex.
And they said all Comic Enterprises wanted was money.
But Judge Wyand said he had concluded that an order forcing Twentieth Century Fox to change the name should be granted.
The judge said such an order was not unfair.
He said Twentieth Century Fox could tell viewers that the newly-titled programme had previously been called "Glee".
"I find it hard to believe that the cost of the re-titling and publicising of the new name would be so prohibitive compared to the value of the series," he said. "I was told many times during the course of the trial how this series is a 'blockbuster'."
He added: "I believe that the balance favours the granting of an injunction in this case."
But he said it was possible that the Court of Appeal would take a different view of the case and rule that Twentieth Century Fox had not breached the trademark.
Therefore he said it was right that his re-naming order should be put on hold until appeal judges had analysed the case.
Comic Enterprises is also seeking damages.
Judge Wyand said it would be hard to assess the amount of money which would be awarded "at the end of the day".
But he said Twentieth Century Fox should make an interim payment of £100,000.
"I do not think that I should deprive (Comic Enterprises) of the advantage of an interim payment," said the judge.
"It should be possible for (Comic Enterprises) to repay the modest sum that I have ordered if my decision is reversed by the Court of Appeal."