I thought someone would have jumped in before now! He was also known as Hom Mooar which means something like 'big Tom, old Tom, Tom senior' -I think that's the gist of it.
As for Hoary it is possibly/ probably a corruption of the family name of that particular Radcliffe branch which was known as 'Y Vayr' or 'Y Voar'. As you will see in Constance Radcliffe's book, the origin of this name is unknown but has been interpreted as meaning 'one who lived by the road'.
As an aside, in Sally McCambridge's book on Andreas there is an explanation Robert Teare's sobriquet - Robert the Hairy! It was in fact derived from 'Robert of the Ayres'. Gotta love the Manx sense of humour.