An interesting interactive description of the etymology of the names of the trigonometric functions:
https://mathisonian.github.io/trig/etymology/
The word sine originally came from the latin sinus, meaning "bay" or "inlet". However, it had a long path to get there. The earliest known reference to the sine function is from Aryabhata the Elder, who used both ardha-jya (half-chord) and jya (chord) to mean sine in Aryabhatiya, a Sanskrit text finished in 499 CE.
Jya, meaning chord, became jiba in Arabic, and was abbreviated as just jb. When the term was translated to latin in the twelfth century, jb was incorrectly read as jaib (meaning "bay" or "inlet"), and thus translated as sinus.
I assume that the Spanish / Portuguese word "seno" just came along as the local translation of the Latin "sinus".