Councillors are being asked to choose a name for a new unitary authority replacing a county council and five district bodies.
Under the new regime Shropshire will be divided into two authorities, an existing one for Telford and a new one for the rest of the county.
The Association of British Counties (ABC) said the title Shropshire Council would be inaccurate.
A borough council lost its judicial review last month against the plans.
Joint legal action
Although the council will serve 90% of the area it will only serve 64% of the population, the association added, as up to 160,000 people live in the Telford and Wrekin Council area.
Names like "Shropshire Heartlands Council" or "Heart of Shropshire Council" have been suggested by the association.
Shrewsbury and Atcham Borough Council claimed at the judicial review, the government acted unlawfully by inviting bids for unitary status and they took legal action with Congleton Borough Council.
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