THE Police Federation has said officers are concerned at proposals to remove the words "Northern Ireland" from the crest on their uniforms.
Mark Lindsay, chairman of the organisation which represents rank and file officers, said any such move would be "problematic".
First Minister Arlene Foster said it was a "branding issue" and Deputy First Minister Michelle O'Neill said the matter would be considered by the Policing Board.
They were speaking after Chief Constable Simon Byrne unveiled a proposed new logo for the PSNI.
Current imagery features the crest - including the words Northern Ireland.
In its place would be two new styles. One, including the crest with the words Northern Ireland, would be used in formal instances such as on stationery, at ceremonial events and on publications.
The other would be the one most seen by the public, under the draft proposals. It features the crest, but the outer band with the words 'Northern Ireland' are removed. It would be used in operational settings such as on uniforms, vehicles, for digital use and on signage.
Both new looks feature the words 'Police Service NI'.
Mr Byrne said he recognised the proposals had sparked a "mixed reaction".
"These proposals reflect the style and tone I set out to the Policing Board upon my appointment about being more visible and accessible. There is a journey to travel before ideas are finalised and presented to the Policing Board," he said.
"The term PSNI is an acronym that has no basis in law and our proposals are based around retaining the crest and the name Police Service of Northern Ireland at the heart of what we do."
The Police Federation said much of the operational proposals outlined by the PSNI "made sound sense".
"It is important that the service modernises and has the ability to adapt to changing circumstances," Mr Lindsay said.
"As clearly outlined by the Chief Constable, this cannot be a name change or a change in the crest as that is set in law.
"There was hard-won political consensus, and considerable internal pain, around the crest when it was introduced. That fact should not be lost.
"We accept that this is an attempt to provide more operationally practical uniforms for officers and greater visibility for vehicles. In fact, the vehicle livery is more in line with what is seen in all other parts of the United Kingdom.
"Altering the crest by removing the name from it is proving problematic. I believe this is inappropriate and it is a view that we will convey during the formal consultation and implementation phase.
"Since the unveiling of the new-look branding, the PFNI is aware of some officers who expressed concern about the removal of the name from the crest that will more frequently be seen in public."
The Policing Board said it was briefed on the proposals at a meeting in May. It said there would be no change to the service's crest or name and will receive a report on the consultation exercise and the associated costs. The Police Federation and Justice Minister have also been briefed.
Former PSNI assistant chief constable Alan McQuillan said the name and crest of the PSNI was enshrined in law and that could not be changed without the Justice Minister setting in process a change to the law.
"The issue of the crest was a very finely negotiated political agreement between the unionist parties then involved and the nationalist parties then involved - essentially the UUP and SDLP," Mr McQuillan told the BBC Nolan show.
"I think there is a desire to be representative to all people and the argument, I think - this is my supposition - is that 'Northern Ireland' is seen by the more republican element in our society as a term they will not use, therefore 'NI' can be Northern Ireland or the north or Ireland and therefore it is acceptable to all."
SDLP Policing Board member Dolores Kelly said there was "nothing to be frightened of" and the consultation responses would be fully considered.
"I think some people are messing about a bit," she said.
"There is no politicking, PSNI, the crest is enshrined in law."
The UUP said omitting 'Northern Ireland' was a mistake and pointed out the St Patrick's cross should be red and not green.
A party spokesman added: "Any rebranding exercise would need to be very carefully explained and be supported by very good reasons indeed."