I'm a Persian, I'm from Iran, and I speak Farsi. Here, we have a very strange rule that we turn آ into و in informal conversations. For example:
خانه = house (formal) /kh a ne/
خونه = house (informal) /kh u ne/
In other words, we mutate a sound based on formality.
I don't know the name of this phenomenon. And I also wonder if we have something similar in English or not?
The shift of classical Persian ān to ūn is a feature of Tehran dialect (Tehrūnī), and of many other forms of colloquial Persian. It is an example of “labialization”. This phenomenon is widespread in languages of the world; we have it in English when we write “all” but pronounce it like “awl”.
I don't know Persian, however I have some knowledge of linguistics. The example given seems to be linked to a shift in register (different use of language in different circumstances). The formal form is 'greater effort'; the informal form is 'lower effort' / more relaxed, which here is a shift from the higher pitched 'a' sound to the lower pitched 'u' sound.
In the example given, this seems to be a semi-generalised rule for this particular sound. I'm not sure if English has similar semi-generalised rules, but something slightly similar would be the general use of contractions. To some people, contractions are a marker of informality and should not be used in highly formal speech or writing.
In general, contractions are dropping or altering specific sounds, which seems to fit with the original poster's request. As well as contractions, some other examples of shifts in register are:
You will note that the informal form is often 'less effort' than the formal form.
However, be careful not to label it 'lazy' or 'incorrect'. Often the formal form is regarded as 'formal' because it is the type of language (dialect) used by the power group in that culture. Formal language is often used as a tool to exclude others from membership in that power group, or to mark out membership / signify access to education / parentage / etc.
Sometimes the use of a differing dialect is deliberate to signify that the speaker refuses to participate in what they see as an unjustified power structure. (Or to signify membership in a different social grouping.)
In Arabic this practice is called "ibdal" (which means conversion) (ابدال).
In Persian the same name is used because:
** I know this from a bunch of Iranian friends.
Another example: انبه (Anbeh) which means mango, turns to امبه (Ambeh) in spoken Persian language.
Though I'm not a linguist, I studied Uyghur and other languages of central Asia for a few years. It sounds like you are describing vowel rounding. Other regional languages such as Uyghur, Kazakh, Turkmen, and others have clear rules for vowel rounding and rounding harmony.
Although vowels in English might be described as rounded or unrounded, it doesn't have the same kind of structures for deciding when a vowel should be rounded or unrounded. For example, words with unrounded vowels don't need to be rounded to become informal, and conjugation won't result in rounded vowels.
