Note that this is not the same as What is it called when words are deliberately spelled incorrectly but pronunciation is kept unchanged? because that question is about deliberate misspellings, whereas this one is about unwitting misspellings.
Many people unknowingly spell an English word exactly as they would pronounce it, which can lead to a misspelling.
Examples:
1.Elifant or Elifent for elephant.
"She ran away on seeing the elifant."
2.Shiwawa for Chihuahua.
"Their dog is a Shiwawa."
This is related to not knowing the correct spelling of the word, and is a common type of mistake made even by native speakers of English, though probably not with 'elephant'; for instance I remember a native speaker cuttingly reject some good advice from a moderator at a car audio forum with the sentence:
You need not lekcher me about the rules of this forum. I am no neofite here.
Sample sentence for SWR:
Writing 'elifent' for 'elephant' unwittingly, based on its pronunciation would be an example of ______________.
The correct term is not transliteration, and google search did not prominently turn up a pointer to such a word:
https://www.google.co.in/search?q=misspelling+words+according+to+pronunciation
So what is the English word for "misspelling words based on their pronunciation?"
A very good option already suggested kindly by @Lawrence is "phonetic spelling" (or phonetic misspelling) but can someone find a single word to express the same meaning?