While helping my daughter read (she is 5) we encountered two names in a story, Thumbelina and Carolina. The way I've come to pronounce the last four letters of "Thumbelina" is "LEE NAH" and the same part of "Carolina" as "LIE NAH". My question is what is modifying the sound "i" makes in each name? Is there a name for this rule? Am I just pronouncing "Thumbelina" or "Carolina" incorrectly?
Thumbelina is was coined by H.W. Dulcken in the 19th Century as an Anglicisation of Tommelise (itself a 19th Century Danish coinage by Hans Christian Andersen) so it could quite possibly be influenced by the sound of the I in that word. It also, being a recent coinage is likely to be strongly influenced just by what people thought sounded better—there was no rule about how to pronounce it until Dulcken's translation came out, so even if he'd said it rhymed with Carolina and people thought it sounded better as is, it would have changed (unless he'd actually written his translation as a rhyming poem, but he didn't).
Carolina - both the states' and girls' name - comes from the Latin form of Charles and are related to the word Caroline as a girls' name, and Caroline as a separate but related adjective form of Charles (hence the adjective Caroline for things relating the the reign of a King Charles).
When adjective forms produced from other words end in -ine we tend to pronounced them with /aɪn/ sounds, and so we would expect a related -ina to be more likely to end up with a /aɪnɑ/ or maybe /aɪnæ/, but we'd be surprised if they ended up /iːnə/. Not very surprised, because it's not like this stuff is always logical, but a bit.
Ironically, in Thumbelina's native language of Danish, Karoline (a common Danish form of Carolina), is pronounced /kɐroˈli·nə/ (say "caroleena" but swallow the R so it's almost "caowleena"—think of the lack of R sound on the end of words ending in R in some English accents) and does come close to rhyming with Thumbelina, but not with Tommelise.
5 Year Old Version:
Normally it's I-NAH, but sometimes it isn't. Thumbelina was first called Tommelise TOM-Eh-LEES-AH, because she's from another country, the same one that the little mermaid is from and where her statue is, and names are the hardest to spell because a lot are from languages other than English, so they work differently. Semolina is funny too, because semolina is just funny.