Wikipedia says: "An 'arms' name can just derive from where the pub actually is" or "Some 'arms' signs refer to working occupations. These may show chaps undertaking such work or the arms of the appropriate London livery company. This class of name may be only just a name but there are stories behind some of them." https://en.wikipedia.org/wiki/Pub_names
From Heraldry,as in "coat of arms".
The sign would have the arms of the current monarch(kings/queens head),a guild(bricklayers/bakers arms)or even a town(Manchester arms).
I've never heard of pubs being under the protection of noble families, and most of those in towns would have no connection with noble families anyway. Other pub names come from the signs displayed, so I can see no reason for the Arms ones being any different. Some of the country ones would actually belong to the estate of the local landowner (who may or may not have been noble), or at least the land the pub stood on perhaps. But the ones with names like Bricklayers Arms would have had no direct connection with the trade, except in areas where certain specialist trades were found, like Colliers Arms, and there only an appeal to the locals would be intended.
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