Chief executive Carole Heatly said some people felt the name carried ''negative connotations'', but others cited an association with quality services.
''We, with our staff, haven't made a final decision on that yet, but will make sure we take everyone's views into consideration before we do.''
Isis, which stands for ''1 Site 1 Service'', is one of the acronyms by which Islamic State is known.
In February, the board said it was thinking of changing the name.
The board is also considering a more fundamental change to how Isis and other Dunedin rehabilitation services operate.
It could involve amalgamating Isis with Health of Older People (wards 6A and 6B) and Mental Health of Older People (ward 6C), but the board is yet to spell out its plan.
It has been consulting unions and affected organisations, but is yet to make a firm proposal.
A feedback discussion paper released by the board talks about basing care on a patient's need, regardless of their age.
New Zealand Nurses Organisation organiser Lorraine Lobb said the creation of a single service on one site was a ''distinct possibility''.
She expected a formal proposal soon, which may entail a loss of positions.
This was likely to be mitigated by impending retirements, she said.
Ms Lobb said the idea of consolidating the services had merit, but would cause concern in some quarters.
''Depending on what it looks like, there will be a level of upset out there, because things won't be necessarily the same, or in the same place maybe.''
Otago Brain Injury Association liaison officer Cathy Matthews said she was not opposed to the idea of changing the services, and wanted to see a firm proposal.
''Like it or lump it, a 65-year-old 30 years ago is quite different to a 65-year-old now.
''In that respect, investing it around need rather than age ... to me, I can see the sense in it.''
Ms Heatly said feedback from staff and other groups would be taken into consideration.
''We have had input from our staff about how to avoid duplication , ensure co-ordination and build on our multi-disciplinary team approach and have specialist practitioners as part of those teams, all of which will improve services for our patients,'' Ms Heatly said.
