Is there a term for the dialect or accent in English in which a typically one-syllable word becomes two syllables?

Factual Questions
101

Short vowels (cat, bed, hit, bought, fuss) have one mora; long vowels (fate, heat, right, wrote, bruise), and diphthongs have 2 morae. Personally, I hear a diphthong in words like “fire,” so I’d say yes, 2 morae in the vowel.

Sometimes consonants can add weight to a syllable, producing syllables with 3 morae-- I’m really not sure, and my mother is not alive to ask, but usually syllables with 3 morae have liquid consonants (which is what R is) and glides (which are sometimes called semi-vowels), because it’s possible to sustain the sound (as opposed to say, an obstruent, like B).

At any rate, yes, 1 syllable, 2 morae in fire.

However, I think fire may just be oddly spelled more than having diphthongs and glides and what have you. I think it is like the word “theatre” in the UK-- spelled “re,” but pronounced “er”; most words in the US (or maybe all-- IAN an expert in UK orthography) that are not agentive but end in “er” are spelled “re” in the UK (centre, litre). However, there are a few words that didn’t get changed when brought to the US, and are still spelled “re” here, and I think “fire” is one.

If it were spelled "fier, we wouldn’t be having this conversation.

102

Thank you for that insight. Fire has been nagging the back of my mind, but I never made the connection to British spelling like “theatre”.

103

I learned from The Diplomat that fire has two syllables in America and one syllable in the UK.

104

“Fier” is an obsolete spelling of “fire”. In both Old English and Middle English, the word was most commonly spelled “fyr” with no “e” at all (though the “fier” spelling begins to appear in Middle English).

The “-tre/-ter” endings of Greek-derived words like “theatre/theater” and “centre/center” are reduced forms of what was the Greek suffix -tron, which turned verbs into nouns.