What is the term that means to add an extra syllable to a word?

The phonological process observed here is anaptyxis, which is the insertion of a vowel. In English, the most common vowel thus inserted is the schwa, as seen in your two examples.

It is epenthesis and anaptyxis, but those are rather vague terms. Epenthesis, in its function, ordinarily makes things easier to say, by breaking up difficult clusters, but the sort of addition being asked about here has an opposite function—it makes something more emphatic and, incidentally, harder to say. So I'd describe it as a fortition; basically as a lengthening, for emphasis.

Resonant consonants, i.e., liquids, glides and nasals, can be prolonged for emphasis. "Brave" -> "Brrrrave!". "Beautiful" -> "beee-youtiful". And a lengthened resonant is interpreted as its own syllable, whose vowel will be the vowel congener of the original consonant, if there is a natural choice of such a vowel. The vowel counterpart of the [j] glide in "beautiful" is [i] -- palatal vowel goes with palatal glide, so that's easy enough. In other cases, the choice of vowel that turns up in the new syllable is somewhat less obvious.

As I recall, this account of these emphatic syllables in English was first suggested to me by my teacher David Stampe.