1911, from German Gen, coined 1905 by Danish scientist Wilhelm Ludvig Johannsen (1857-1927), from Greek genea "generation, race" (from PIE root *gene- "give birth, beget"). De Vries had earlier called them pangenes. Gene pool is attested from 1946.
1889, from German Chromosom, coined 1888 by German anatomist Wilhelm von Waldeyer-Hartz (1836-1921), from Latinized form of Greek khrōma "color" (see chroma) + -some (3)). So called because the structures contain a substance that stains readily with basic dyes.
<a href="https://www.etymonline.com/word/genome">Etymology of genome by etymonline</a>
Harper, D. (n.d.). Etymology of genome. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/genome