This is an early medieval English surname. It is arguably a metronymic, that is to say a surname derived from a mothers name rather than the fathers. Less than one percent of all surnames do have such an origin, so it is rare, if not quite unique. In this case the prefix "Bea" is believed to originate from the early female name Beatrice, also found in such surnames as Beaton, however this is not proven. In the case of Beacock it would seem to be a diminutive metronymic as shown in the recording of Henricus filius Becok in the Subsidy Tax rolls of Lancashire in the year 1332. This would seem to translate as Henry, the son of Beatrice's son. Presumably the original Beatrice was a land owner in her own right, and her son took her name rather than his fathers. Later in 1366 we have the recording of John Bekokson again in the Subsidy Tax rolls of Lancashire. Assuming he was related he may well have been Henry's son and hence the great grandson of the original Beatrice. To show that the surname was not created by one family but arose in various places, we have an earlier recording,being that of Stephen Becok of Oxfordshire, in the Hundred Rolls of landowners of that county in 1279.