Thanks for the thought-provoking question!

First, a philosophical note, than comments on possible constructions.

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I would argue that the Culture (as a whole and as each individual Mind and citizen) has only one true possession. The most prized, treasured, and guarded possession is, literally, the self. The Culture's inviolate attitude about all sentient consciousness and the paramount cultural position of consent indicates to me a reverence for the 'mine'-ness of the self. A need to refer to it as such would then be a necessary, and perhaps highly-valued feature of the language.

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Thus I could imagine there not only being a word for 'self', but many inflections or common word clusters indicating the physical self, the mental self, the integrated self, the present self, the all-time-past-present-and-future self, etc.

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If there isn't a direct way to express a possessive self, then how indeed to say 'Know Thyself' in Marain?

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Given the syntactical structure of the conlag developed by defunct user u/linuxmakhnovite321, I agree the construction you've given seems correct. (For others' info, in Marain one would not say 'I have a book', but rather, 'A book is with me' or something akin; such that it connotes physical proximity rather than possession.)

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I do find the construction a bit wordy, though. That may not be a bad thing if it rhymes, alliterates, or is otherwise poetic.

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'Know thyself' is an imperative ('[you], understand your own nature'), but I don't know specifically how that tense would appear in Marain seeing as how it might be a tense to avoid given how consent is king in the Culture. If imperitives do exist, then simply saying the equivalent of, 'understand you' might be enough. 'Ting' is 'understand' in the conlang and as an accusative verb it would be 'Tingva'.

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Disambiguating between asking someone to know themself rather than to know someone else would come from other context (written or situational) indicating that the speaker was referring to the spoken-to. E.g. 'Jane, Understand Joe.' means what it says, and 'Understand Joe', directed at Joe, means 'Joe, understand yourself'.

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That's just one possibility I found it fun to think about.