A grammatical point of view about the possible valid meanings of the term anātman
Nairātmya (the view “there is no ātman”) is a word used by later Buddhists and they equate it to anātmatā (meaning “the state of being anātman”) which is a term (used in the Pali canon and other early texts) supposedly by the Buddha.
However there are two types of negation possible using the particle ‘na’:
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Paryudāsa-pratiṣedha (i.e. exclusion, or negation with a view to exclude) - here the particle ‘na’ when compounded with a following noun (such as in the compound ‘an-agāriyam’ for example) gives the meaning of “something else except agārīyam” or “something that is not agāriyam” (agāriyam is excluded by the compounded prefixing particle ‘na’). Another example: na+brāḥmaṇa = abrāhmaṇa (one who is not a brahmin, brahmins are excluded from the definition). Yet another example: na+āgata = anāgata (one that has not yet come; anything that is ‘āgata’ is excluded from the definition of anāgata). This negation with intent to exclude also applies to the term anātman (i.e. anything that the term anātman/anattā describes cannot be considered to be ātman/oneself/I/me/myself)
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prasajya-pratiṣedha (simple-negation) - When ‘na’ is used as an independent word (along with a verb) it gives the sense of a simple negation. So for example, ‘devaṃ na namāmi’ means “I don’t honour a deva”. But when used as the first member of a compound the meaning changes from simple negation to exclusion - a-devaṃ namāmi “I honour someone other than a deva”.
In Buddhism an-ātman therefore originally (in canonical usage) has the meaning “something else that is not oneself/me/myself i.e. something else which is not ātman” - but not a simple negation of the existence of ātman (nairātmya).
The Buddha according to the Buddhist canonical texts was not therefore a nairātmya-vādin (one who says there is no ātman) but an anātma-vādin (one who says ‘this is not the ātman’ i.e. ‘this is not your self’ or ‘this is not who you are’).
This can be empirically tested. Nowhere in Pāli/Sanskrit can ‘na’ prefixed within a compound be considered a pure negation of existence of that substantive.