We don't have synonyms for eye dialect yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are yue dialect.
(n) :
(uncountable) Nonstandard spellings which, although they indicate a standard pronunciation, are deliberately substituted in place of the standard spellings, often to indicate that a speaker's regular use of language is nonstandard or dialectal.
(n) :
(countable) A set of such nonstandard spellings, collectively used to reflect a certain form of speech.
(n) :
(uncountable) Nonstandard spellings which, although they indicate a standard pronunciation, are deliberately substituted in place of the standard spellings, often to indicate that a speaker's regular use of language is nonstandard or dialectal.
(n) :
(countable) A set of such nonstandard spellings, collectively used to reflect a certain form of speech.