The Vidella Hotel's owners recently adopted the new moniker - along with the slogan "We will keep you up all night" - as part of a rebranding.
But the change has met with stiff opposition in some quarters.
A spokeswoman for Pfizer, which sells the erectile dysfunction pills, said it would be "taking appropriate action".
"Pfizer does not support nor condone the use of the Viagra trademark in this manner," she said.
"In the UK advertising of prescription-only medicines to the public is strictly prohibited."
Owner Neil Marshall said it was intended to reinforce the hotel's image as a budget destination.
He said previous guests had expected an upmarket hotel when they arrived.
"The Vidella had quite a bad name to it - and the type of clientele coming here thought they were going to come into a posh location," he said.
No complaints had been received, and lots of guests had found the new name funny, he said.
"It'll probably put off the family element but I don't like lying to people, when they come in here they know what they are walking into - friendly all the time but we are a budget hotel.
"If you're not game for a laugh, don't come here."
Claire Smith, president of hotel organisation Stay Blackpool, said the name change was "opening yourself up to problems".
"As a publicity stunt, good on him - but going forward...you may be potentially putting off good quality guests."
"My only concern is you're going to get some real weirdos that are going to not take it in the context that it's meant - in that they're just going for a laugh - and the good hoteliers are going to be spending the whole time just trouble-shooting."
Hoteliers in Blackpool have said they fear a guesthouse which has been renamed The Viagra Hotel will attract "weirdos" to the seaside resort.