Former PC Joel Borders, 45, from Preston, and serving Metropolitan Police constables Jonathon Cobban and William Neville face a two-day trial on July 28.
They are alleged to have shared racist and misogynistic messages with then-serving Met officer Couzens, 48, who is serving a whole life sentence for the kidnap, rape and murder of 33-year-old Ms Everard in March 2021.
The three defendants appeared in the dock at Westminster Magistrates' Court on Wednesday charged with sending grossly offensive messages on a public communications network between April 5 and August 9 2019.
Their identities were initially kept secret when they were charged by postal requisition in February.
Cobban, 35, from Didcot, Oxfordshire, and Borders both face five counts, while Neville, 34, from Weybridge, Surrey, faces two counts.
They spoke to confirm their names, addresses and dates of birth and entered not guilty pleas to each of the charges during a hearing lasting about 20 minutes.
Nicholas Yeo, defending, said the issues in the case were "whether or not the messages were grossly offensive" and "whether or not the defendants had the Mens Rea to intend to be grossly offensive".
The court heard that evidence will include training courses the officers attended to assess whether they "should have known the content of the material they were exchanging was grossly offensive".
Chief Magistrate Paul Goldspring granted Cobban, Neville and Borders unconditional bail.