What are the two parts of SHA1's compression function called?
The part where 16 words are expanded into 80 words is often called message schedule (the name in FIPS&nbsp;186-4) or message expansion; that's also the key expansion phase of the cipher at the core of the compression function (SHA1's message block is the key of that cipher, due to the Merkle-Damgård + Davies-Meyer structure of SHA-1).

The rest of the compression function would be the compression itself; or the encryption step of the cipher followed by the Davies-Meyer final combination (which, in SHA-1, is five additions modulo $2^{32}$, rather than XOR).