I know of no term from prosody for the repeated use of a syllable at the beginning of successive words, but I imagine that there must be one.
In absence of a term from prosody, you might call this a reduplicated syllable or a reduplicated initial (syllable).
Reduplication is a technical term from linguistics to describe syllable or root compounds like "papa" and "pee-pee" which compound the same syllable or root twice. A subtype of reduplication is rhyming reduplication, which encompasses phrases like
hokey-pokey, razzle-dazzle, super-duper, boogie-woogie, teenie-weenie, walkie-talkie, hoity-toity, wingding, ragtag, easy-peasy (See here)
Your example of
Carla Carlucci
seems akin to the rhyming reduplication examples, except that the reduplication happens on the initial syllable. This is why I suggest initial (syllable) reduplication.
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