Would it have been a case of
'Dyas-muhan'? Nah, how about 'Desmond'?
or would it have been a more natural evolution of pronunciations?
Would I be better off asking a linguist?
You would probably be better off with /r/asklinguistics. But your question is also quite unfocused - anglicisation of what? when? where?
Do you mean specifically of names into English?