Whether or not there is a "better" term depends on your audience, and how annoyed they will be if you use the "wrong" term, according to their beliefs. You have apparently decided that this is to be analyzed as insertion (as opposed to deletion, or suppletion): where do you think this consonant is inserted? In the morphological component? In the phonological component? Or are you not concerned with synchronic analysis, under some particular theory?
"Epenthesis" is the broadest term for insertion ("insertion" is another obvious term for "insertion", perhaps also "intrusive" or "linking" as adjectives). You could use the term "prothesis" which specifically limits it to beginnings of words, but few people actually use that term. Wikipedia claims that "excrescence" is consonant insertion, but that doesn't match actual usage in the literature (that term is used neutrally w.r.t. what kind of segment is inserted, instead it's more about the phoneticness of the process).
In the phonological literature, it is not considered an impediment to using the term "epenthesis" if the conditions on insertion are partially morphological or syntactic. Obviously, though, if the process takes place in the syntax then it's not in the phonology, so any such case would not be dealt with in the phonological literature (and it would be distinctly strange to call anything in the syntax "epenthesis").