'carnation-pink' is a compound formed in Modern English from 'carnation' + 'pink'. 'carnation' originates from medieval Latin 'carnationem'/'carnatio' (from Latin 'caro, carnis') where 'caro' meant 'flesh' and referred to a flesh-colored (rosy) hue; 'pink' as a color name comes from the flower name 'pink' (Dianthus), used in English from the 16th–17th century to name a light red/pink shade.

'carnation' came into English via Late Latin/Medieval Latin ('carnationem') and Old French forms and was used to describe a flesh-colored (rosy) hue; 'pink' originally named the small flowering plant and later the color associated with that flower, so 'carnation-pink' developed by combining the flower name and the established color term.

Initially 'carnation' referred to the flower (and by extension a flesh-like/rosy color) and 'pink' referred to the flower and its color; over time the compound came to specify a particular pale/rosy pink hue now called 'carnation-pink'.