The Conservative Campaign Headquarters press office account was renamed "factcheckUK" during Tuesday evening's ITV broadcast, offering commentary on Labour leader Jeremy
Corbyn's statements and retweeting messages supporting Boris Johnson.
The @CCHQpress account is verified by Twitter, displaying a blue tick which is intended to denote that a user is genuine.
The Liberal Democrat press office posted an image suggesting they were reporting the account to Twitter for "pretending to be me or someone else".
'Trust in politics eroded'
They tweeted: "And people wonder why trust in politics has been eroded @CCHQPress"
Labour's David Lammy tweeted: "The Conservative Party press office @CCHQPress rebranding themselves as 'FactCheckUK' shows what disdain this party and this government has for the truth."
"The Electoral Commission must investigate and punish this blatant attempt to decieve the public."
Meanwhile, some other Twitter users also changed their display names to factcheckUK and posted critical comments about Mr Johnson.
Others changed their display name CCHQ Press Office, while Tony Blair's former spokesperson Alastair Campbell changed his display name to Boris Johnson and tweeted: "I won't get Brexit done #FactCheck"
The Twitter display name was changed back to CCHQ Press shortly after the debate ended. The Conservative Party has been contacted for comment.
Tory Party chairman James Cleverly told BBC2's Newsnight: "The Twitter handle of the CCHQ press office remained @CCHQPress so it's clear the nature of the site.
"The reason we did that is because we were calling out the inaccuracies, the lies that were coming out during the debate. The NHS is not for sale."
He replied "I disagree" when told the party had been misleading the public, and said the change would have been an idea from the party's "digital team".
Asked if he knew about the change, Mr Cleverly said: "The digital team have got a remit, I set that remit, they work within the remit and I'm absolutely comfortable with them calling out when the Labour Party puts what they know to be complete fabrications in the public domain - and we will call that out every time they do it."