The five syllables, na-mah-shi-va-ya, are not a Vedic phrase lifted whole. Namah shivaya as a dative phrase, homage to Shiva, occurs within the Shri Rudram in the Taittiriya Samhita of the Yajur Veda, itself compiled by roughly 1000 BCE, but the Shri Rudram addresses Rudra across many verses and does not isolate this formula as a stand alone mantra. The panchakshara as a discrete five syllable unit, prefixed with Om and chanted on its own, is a Shaiva devotional development, current by the medieval period and carried forward through the Shaiva Siddhanta and Virashaiva traditions of South India, where it became close to a confession of faith. Basavanna and the twelfth century Lingayat poets built entire vachana verses around it, and it travelled from there into pan Indian and then global use through the bhakti movements and, in the twentieth century, through teachers who taught it to non Indian students as a standalone chant.
The grammatical reading is not disputed among Sanskritists: namah is homage, shivaya is Shiva in the dative, auspicious one to whom homage is offered. What is genuinely contested is a devotional reading that entered circulation through modern Siddha Yoga commentary, which glosses each of the five syllables to one of the five elements, na to earth, ma to water, si to fire, va to air and ya to ether, so that the mantra becomes a map of the created world folding back into Shiva rather than only a sentence of homage. Some teachers in that lineage also offer a wordplay on na and mama, not mine, reading the mantra as a renunciation of ownership rather than a grammatical parse. Sanskritists treat both as devotional elaboration laid over a plain dative phrase, not as alternative grammar.