In a word, No. The oldest extant copies of the books of the New Testament are in Greek, and none of these use the Hebrew divine name ‘YHWH’. Because NT writers who quoted the Old Testament almost always cited a Greek translation rather than the original Hebrew text – 340 times out of 373, according to Archer and Chirichigno  – quotations of OT verses that include the divine name in Hebrew are rendered in the NT using kyrios, or Lord; e.g. Mt.3:3.[2,3] The divine name does not appear in the NT.
A shortened form of ‘Yahweh’ or 'Jehovah,' however, is found in many Hebrew personal names (e.g. Jehoshaphat = "Jehovah has judged"), and some of these appear in the NT. Unfortunately, the already shortened ‘yah’ was often nearly lost in transliteration into Greek, as for example with Mattias for Mattithyah (Matthew), Elias for 'Eliyah (Elijah), and Ēsaïas for Yĕsha`yah (Isaiah).
Some of these Hellenized names regained a stronger connection to YHWH when translated into English; e.g. Elijah (Jn.1:21) and Jeremiah (Mt.2:17). So too for the Greek name Iesous (for the Hebrew Yēšūă), though only the two times it is translated as Joshua (Lk.3:29; Ac.7:45), not the 972 times it is rendered Jesus, the same name in Hebrew and Greek.
The ‘yah’ connection is also lost, then found, with the transliteration of the Hebrew ‘Hallelu Yah’ (literally, ‘Praise Yah’, e.g. Ps.105:45) into the Greek ‘äl-lā-lü-ē-ä' in Revelation 19, which is often transliterated again into English as ‘hallelujah’.
These shortened forms hidden in the NT are not the divine name, but they do point it, though often less obviously so in Greek than English.