Normally they are written as nāmakāya and rūpakāya.
I did a search on Sutta Central for them and the search results:
“6 results for nāmakāya AND rūpakāya”
As you see, no suttas explain the terms. They are in the original commentaries.
Here is the relevant part in “1.3. Ānāpānassatikathā” (just below the middle of the page):
“Kathaṁ “sabbakāyapaṭisaṁvedī assasissāmī”ti sikkhati, “sabbakāyapaṭisaṁvedī passasissāmī”ti sikkhati? Kāyoti dve kāyā—nāmakāyo ca rūpakāyo ca. Katamo nāmakāyo? Vedanā, saññā, cetanā, phasso, manasikāro, nāmañca nāmakāyo ca, ye ca vuccanti cittasaṅkhārā—ayaṁ nāmakāyo. Katamo rūpakāyo? Cattāro ca mahābhūtā, catunnañca mahābhūtānaṁ upādāyarūpaṁ, assāso ca passāso ca, nimittañca upanibandhanā, ye ca vuccanti kāyasaṅkhārā—ayaṁ rūpakāyo.”
So, “nāmakāya” is basically vedana, sanna, sankhara, vinnana, or the four rupakkhandha.
And “rūpakāya” is rupakkhandha.
This section is in the description of “Ānāpānassati”.
– As you can see Ānāpānassati is not about breath!
I have tried to explain these ideas in simple terms in many posts:
“Search Results for: anapanasati”