Learn English – A word/phrase for “voice change”

The term that comes closest to what you're looking for is either trips or round trips.

A trip is a journey. A round trip is a journey that starts and ends in the same place. So if you start at home, travel to Paris, and then come back home, you have made a round trip to Paris.

In many cases, the "round" nature of a trip is implied. So the most common way of expressing what you're talking about would be:

You want to get a driving license? Oh, that's a pain. You'll have to make at least three trips.

The idea of multiple trips already, depending on context, carries some mild sense that the trips are a burden. If you use "round trips" instead, it emphasizes this:

You want to get a driving license? Oh, that's a pain. You'll have to make at least three round trips.

As best I can tell, this is the most idiomatic way to express what you're looking to express.

In English, unfortunately, I believe we have no single verb that exactly conveys the negative sense of the Farsi منت گذاشتن

Obligate is a verb which in itself connotes nothing negative. Dictionary.com defines it as to bind or oblige morally or legally. Nevertheless, it is sometimes used in a negative sense, thus:

I understand that this is a great favor but please stop trying to obligate me.
Today I asked my colleague to help me and he did but not without making me feel obligated.

Another useful English word to consider is the adjective beholden. Although this word means only indebted or obligated, it is seldom used except in constructions which do connote something negative:

I understand that this is a great favor, but please stop trying to make me beholden to you.