I checked out the glossary Arnold linked to and didn’t find the answer, but I did find out what Yoda has been using:
ANASTROPHE (uh-NAS-truh-fee)
The inversion of the natural or usual syntactical order of a pair of words for rhetorical or poetic effect, as “inspired he was” for “he was inspired.”
The best I can come up with is paragoge, the addition of a non-semantic sound or syllable to the end of a word. In one reference (Orthometry; the art of versification and the technicalities of poetry, with a new and complete rhyming dictionary, by R. F. Brewer, B. A, published in Edinburg, 1925), I found this word used more specifically to refer to the addition of a syllable to complete the meter of a verse, but not the rhyme. I e-mailed 3 people that I thought might know a better answer. Two replied but were of no help. The third never answered.
This device seems to be especially common with the dactylic rhyme, which is neither masculine nor feminine. It is a treble rhyme with the accent on the antepenult. Popsicle/stopsicle and Finnegan/chin-g-gan are both examples of dactylic rhyme. The dactylic rhyme is usually associated with humorous or nonsense verse because the difficulty of finding rhymes often leads to absurdities. At least one serious poem has used the dactylic rhyme, The Bridge of Sighs by Thomas Hood. Nonsense syllables are de rigueur in the double-dactyl verse form.
I remember reading (in The Princeton Guide to Verse or a book with a similar title) that in some ancient British poetry, an /n/ was sometimes added to the end of a line to match the rhyme. I can’t remember if this was in Middle English or in Welsh. In the book, the practice was referred to only as nunnation. (Nunnation means the adding of an /n/ to the end of a word for any reason.)
I’ll include the text of “Poemsicle” in case anybody was really interested.