Q. Why does Advaita Vedanta more commonly refer to ‘Self’ rather than ‘no-self’?

Tom: it is because the Non-Dual Reality that we Truly Are is only discovered when we turn towards the sense of ‘I’ or ‘I AM’, otherwise known as ‘Self’. This is the single factor that leads to realisation.

The language of the teaching is there to facilitate the method of discovery of the Self that we truly are, and this discovery is Total Liberation.

How so?

By stating that we are the Self, we are encouraged to discover this for our self in our own experience, and so turn our attention selfwards, ie. towards the Subject or ‘I AM’. When that Self that we are is discovered, only then do notions of Self or no-self themselves become obsolete (ie. in self-realisation there is no concept of self or true self or even of self-realisation).

For those who are interested this is explained in detail in the book The Path of Sri Ramana – Part 1, especially in Chapter 8

Here are 2 verses from Sri Ramana Maharshi (taken from the text Guru Vachaka Kovai):

393.One who has wisely chosen the straight path
Of self-enquiry can never go astray;
For like the bright, clear Sun, the Self
Reveals itself direct to whoso
Turns towards it.

391. Those who do not dive into the Heart
And there confront the Self in the five sheaths hid
Are only students answering out of books
Clever questions raised by books,
And not true seekers of the Self.

Many more verses like this can be found here.

Also see:

Q. Why turn within? Nonduality as I have experienced it is the actual disappearance of what is considered within and without, one seamless blending