Recorder Sophie Drake refused an application by Griffiths's barrister, Paul Flaming, to impose a reporting restriction under the Contempt of Court Act 1981.
Mr Fleming claimed an order should be made as reporting details of his home address would put him at risk due to his previous occupation.
He said: "I cannot demonstrate a particular risk from particular individuals.
"I can merely draw upon the nature of the work that was done and sheer number people he had encountered over many, many years."
The Yorkshire Evening Post made representations to the court opposing the application.
Rejecting the application, Recorder Drake said: "In my judgement Mr Griffiths is in no different position from any other police officer who is charged with an offence.
"He is in no different position from any man charged with possessing indecent images of children.
"We have a system of open justice in this country and to restrict the publication of details that relate to a case is very much an exception to the rule of open justice.
"There has to be a very good reason for that to happen.
"In my view, I see no good reason for that to happen."
After the case Chief Superintendent Julie Sykes of West Yorkshire Police’s Professional Standards Department, said: “ West Yorkshire Police requires all its officers and staff to adhere to the highest standards and any alleged criminal behaviour is fully investigated, as has been the case here.
“Officers began an investigation as soon as evidence regarding Griffiths’ offending came to light, resulting in court summons being served upon him.
“He subsequently resigned from the organisation before the case came to court and has now been dealt with for the offences he subsequently pleaded guilty to.
“Griffiths behaviour in accessing such vile material was absolutely abhorrent and he was arrested and suspended as soon as these matters came to our attention.”