Facing calls for the city to address its historical connections with the slave trade, Liverpool Mayor Joe Anderson said it wasn't clear that Penny Lane's name was derived from the notorious slaver.
"My understanding is that there is no evidence that "Penny Lane" is named after slave trader James Penny," he said on Twitter.
"It is debated and said that there was a toll bridge that cost a penny there hence its name."
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The street currently appears on a list of Liverpool streets associated with slavery, which is on show at the city's International Slavery Museum.
Richard Benjamin, head of the museum told the Liverpool Echo: "We realise that there is some debate about whether Penny Lane was named after James Penny and we openly talk about this to visitors.
"The research that was carried out in 2007 - the year that the museum opened - was indeed not conclusive, but we have not removed it from our collection, as we believe the museum is a place of debate and discussion.
"We are actively carrying out research on this particular question and will re-evaluate the display, and change if required."
Local councillor Richard Kemp told the Echo the damage was "disgraceful".
He said: "I'm really annoyed about this, this is just based on a rumour that has gone around that Penny Lane is named after James Penny - which just isn't true.
"If it was the case then that would be something to be debated and discussed, but it isn't - so this mindless graffiti is just disgraceful."
