One reason why these are considered by some to be single segments is that they simplify to [w l n ...] in some dialects. There are sub-trends in phonology which treat consonant plus glide sequences as rounded or palatalized consonants. I am not persuaded by those claims, but that's not the question. If we assume that these are single segments, then the best standard term that unifies them is "complex". More often, we talk about them with a phrase, like "consonant with a secondary / vocalic articulation". "Double articulation is usually reserved for consonants with two primary articulations, such as kp, gb, and clicks. "Double consonant" is usually reserved for geminate consonants, which are two exactly same consonants, or a "long" consonant.
The evidence for the analysis of "hw" is very weak. It only appears where [h] can appear. It varies with plain w. There is also "hj" as in human, hubris. I know that some people pronounce human as "Yuman", so this simplification may be broader than just applying to h. The variable glide [j] in new is missing my dialect, but I have the voiceless or aspirated glides in white and human. The peculiar distribution of postcontinental palatal glides as in human, where the following vowel is always [u], has led some people to treat that as a diphthong [iu], so "new" would be [niu]. There is not a particularly strong reason to treat all of these consonant plus glide sequences the same way in English.