As a deity name
Name 42 of the Gayatri Sahasranāma — Devi Bhagavata Purana, as taught by Sages
As a Hindi name
No reading on this path — this spelling has no entry in our Hindi sources, and no near neighbour is attested there either. We say so rather than invent one.
As a Sanskrit word
Meaning
a spiritual preceptress, [The title ācārya affixed to names of learned men is rather like our ‘Dr.’; e.g. rāghavācārya, &c.]
Scripturally attestedWhy this matches what you typed
M1 · same meaning "ācāryāyai" is the dative of "ācāryā" — the same word in a different grammatical case.
Dictionary citations
ācāryā (ā), f. a spiritual preceptress, Pāṇ. iv, 1, 49; Siddh. [The title ācārya affixed to names of learned men is rather like our ‘Dr.’; e.g. rāghavācārya, &c.]
Caveats
Sources contain errors and engines have limits; every claim above carries its citation so you can verify it. This is guidance about names and their sources — not religious or astrological consultation. How we work · Our sources