Looking at the IGI, an alternative spelling is Meshach, or Meshick, or Mesech.
Meshach, in the bible, was 'the title given to Mishael, one of the three Hebrew youths who were under training at the Babylonian court for the rank of Magi (Dan. 1:7; 2:49; 3:12-30)'
There is a Mesech Rice b. 1813 Fifehead Magdalen, Dorset, England, parents Mesech and Elizabeth.
Some information on Mesech Sr:
The cottage now called Mandy cottage, at the corner which was then known as the Crossroads, was in 1840 occupied by a farm labourer named Meshach Rice, who was to live there until his death in 1866 at the age of 85. He was born in West Stour and came to live in Fifehead upon marriage. His wife was a member of the Slade family, who had lived in the cottage for generations and whose menfolk had been the village tailors over many years. It was appropriate that a man called Meshach should come to live in the cottage because the names of two of the Slade tailors had been Shadrach and Abednego. Meshach Rice was an agricultural labourer for most of his life but in old age he was employed as a gardener at Fifehead House.