I recently received the above question and I asked our good friend Slowhands what his answer to it was. The following is what Slowhands had to say on the subject. If anyone has anything to add then please share it with us.
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Very good question.

There are many theories about the name. The most factual seems to relate to
the Doomsday book entry ( around 1070 ad) for Dean Magna ( Dene Magna) or
Mitcheldean, and marks what is probably the first recorded use of Dean ( or
Dene, or Deane ). This would relate to a Manor of Dean as an administration
/ organisation centre in the area we know as the FOD.

Of course we know the Romans worked iron in the Forest and before them we
have evidence of Stone age and Iron age occupation. So who gave us the name
Dean ?

One theory is that Viking raiders were left in the area and named the local
asset Dane Forest, I'm not convinced by this but it has romantic
attractions !

Another theory is that it is derived from the ancient Saxon words "Denu" - a
valley or "Den" - a wood, which I probably think more likely, given the
topology and natural tree covering. Deenhill or Edge Hill is probably the only toplogical feature to have a recognisable Dean attribute.

The Royal label relates to the declaration of the area being a Royal Hunting
ground, this predates any notion of loyalty to the Crown.

regards

S