The Methodist Church alas was one of the factors which led to a weakening of the Manx culture.
Many people blame the 1872(?) Education Act brought in by Governor Loch and Sir James Gell for being another large nail in the coffin. No Manx was allowed to be spoken in school whatsoever.
In my family, the next generation was not taught to speak their mother tongue & parents kept it for private conversation. These were children born between 1885 and 1910.
Anglicising of names has been going on for a lot longer. It is very instructive to look at Christian names - Rev. Prof. R.E. Thomson wrote a very helpful article about the formation of Manx surnames from christian names.
One of the worst features of anglicisation is the coining of inappropriate placenames + adoption of solicisms such as "Laureston Manor" Ballacriy Manor etc
Good luck with your researches