Derivation of Gateshead as a Place Name

 The derivation of Gateshead as a place name is that it’s the Northern end of the Bishopric of Durham, located at the head of the road (gate) from Durham. Gate is a Norse word meaning road or lane and it is still found throughout the North of England as a street name. Indeed, Gateshead's earliest streets were Pipewellgate, Oakwellgate and Hillgate.
There are 25 examples of gate meaning road in York and a further 5 have been lost over the years. Colliergate where coal was once sold is but one example.You can find them all here  If you follow that link you’ll find that roads in York that actually pass through gates in the city walls use the additional word “Bar”.
  In Leeds the bus lanes are, even today, called bus gates.

Along the way, the Gateshead local authority, chose not to have a gate as a symbol but a goats head. As a child at Gateshead Grammar School I never felt right walking about Gateshead with the Goats Head on my blazer. Even to a schoolboy it seemed ungrammatical, not to mention corny and naff. Since local government reorganisation in 1974 Gateshead does now use a gate ( a portcullis) and a head (represented by a helmet) in both its formal coat of arms and its “logo”

The idea that there was a headland where goats grazed is piffle. Or rather that there were a few goats grazing, as there were all over Britain, should lead to the name is piffle when there's a much better explanation, just given above. Gateside was an alternative name used, perhaps by Newcastle folk and it may be that at that time there was a physical gate on the Tyne bridge
For a bit more on the derivation of Gateshead as a place name