What is the best translation of Anatta into English? Is the best translation of Anatta "non-self" or "there is nothing that you can take as me, mine, self or non-changing everlasting controllable part which can be identified as me, mine or everlasting core" or something else based on the interpretation of different lineages?
CORELESSNESS

Before we can pick a translation we must understand what it is that we are translating.


Prefix an- is a simple negation.
Hindu concept of Atman should not be confused with Aham (the simple reflexive "I", "ego" or "self") nor with Jiva (the vitality that makes an animate being an animate being). Atman means "inner spirit" or "core" and refers to what is supposedly the unchanging subject of experience, also known as "The Knower of the Field" (Purusha), and the source of its own activity. Basically, Atman is that fictitious little boss that sits in our head, looks through our eyes and decides what to do.
Pali ending of -tta often corresponds to English -ness:



  -tta: expresses the state, nature or quality of being that which is denoted by the adj. or noun: puthujjana, a common man +tta=puthujjanattaṃ, the state of being a common man; buddha, a buddha +tta=buddhattaṃ, Buddhahood; atthi he is +tta=atthittaṃ the state of "he is", existence.


From these three, the word can be translated as no-spirit-ness, or in proper English spirit-less-ness -- but such rendering is misleading. First, because in English "spiritless" has connotations of weak, demotivated and barely alive. And second, because Buddhism does not exactly deny "spirit" as an abstract aspect of relationships and interactions.

Another option is to take Atman as "subject" and render anatta as subjectlessness. This choice sounds true to the original meaning, but directly contradicts the western understanding of experience as comprised of subject and object.

A philosophically more correct option IMO would be core-less-ness. This matches both a simple understanding of anatta as an absence of substantial independent self in sentient beings, but also the wider Madhyamika philosophy which postulates that all entities are contextually defined imputations lacking any kind of self-identical ontologically existing core.

P.S. In western philosophy the notion of corelessness is sometimes identified with Bundle Theory of David Hume. Also, the relationship between observation and delineation of entities is one of the major topics of Hierarchy Theory.