The Taamei HaMinhagim, in "הנהגות אדם בבוקר" says:
ג טעם שתקנו רז״ל לומר על נט״י בנוסח ברכה זו לשון נטילה, מפני שהוא לשון
הגבהה מתרגום "ותשאני רוח" "ונטלתני", וכתיב (ישעיה ס"ג) "וינטלם וינשאם כל ימי
עולם" - שצריך שיגביה ידיו למעלה (שלחן ארבע) :
ד עוד טעם לפי שצריך ליטול מן הכלי והכלי שמו נטלא בלשון תלמוד. אבודרהם:
That is, that according to the Shulchan Arba it is called that because Netilah means "raising", and you have to raise your hands after pouring the water on them, and according to the Abudirham it is because the vessel with which you pour the water is called a Natla in the Talmud (see in Chulin 104a: "נטלא בת רביעתא").
The reason being that it is done with a vessel called a natla, antal, or antil, cited in the other answer, is stated by numerous early Rishonim, including Raavya (Teshuvot Uveiurei Sugyot 1109) quoting R. Hai Gaon, Arukh (נטל), Rashi, (responsum 266 and Likkutei HaPardes pg. 11a), Raavan (Hulin 271), Rokeah (Commentary to Siddur: al Netilat Yadayim: page 4), Seffer Hassidim (58 in ed. Margolis), Manhig (Hilkhot S'uda pg. 204) and others.
In addition to citing this explanation, Sefer HaPardes (of R. Hayyim Navyu in Sha'ar HaMaaseh: Birkat Netillat Yadayim) cites a similar explanation, that netillat means taking, and refers to taking the vessel.
Meiri also cites the explanation that "netillat" is a reference to the vessel, known as a natla (Berakhot: Kundres Beit Yad s.v. netila), but he also cites another explanation (mentioned in the above answer), that the term refers to raising the hands done when washing. This is also quoted by Shibbolei Haleket (Seder Berakhot 136) and Rashba (Shu"t 7:534) in the name of R. Hai Gaon. (In apparent contradiction to Raavya's reference to R. Hai Gaon).
HaKtav V'HaKabbalah (Leviticus 11:44) gives an additional explanation: that the hands are spiritually elevated through the washing, hence the term 'netilla'; raising.