Words that result from a gradual distortion of other words

Solution 1:

The term sometimes used is corruption.

Solution 2:

There are many factors and processes at work here, just one of which is anglicisation:

Anglicisation or anglicization is the process of converting oral or written elements of any other language into a form that is more comprehensible to an English speaker; or in general, of altering something so that it becomes English in form or character. It is also called anglification, anglifying, or Englishing. The term most often refers to the process of altering the pronunciation or spelling of a foreign word when it is borrowed into English. Personal names may also be anglicised. This was rather common for names of antiquity or of foreign heads of state, and it has also been common among immigrants to English-speaking countries (for example, Battenberg became Mountbatten).