I've recently returned from the UK and IOM and was able to spent quite a few hours over a couple of days in the Manx Library. The staff were extremely helpful and I had some good results.

GG grandfather William Morrison was born circa 1822 in Ballaugh according to the 1851 Santan census.

No William Morrison was found in Ballaugh baptism records but a William, son of Patrick Mylvorrey and Ann Cleater, was in 1822.

Interestingly Patrick Morrison was found to have married Ann Cleater in Ballaugh in 1815.

So it seems that the Anglisation of the name was occurring about this period with Morrisons appearing afterwards and Mylvorreys before that time.