John-
Thank you dearly for getting back to me so quickly.
Many Paleologo most certainly used Colaianni as a name. I will email you over 50 scholarly sources (history books all housed at Harvard, Yale, University of California, etc). if you'd like.
My interest in this family is as a researcher. They're connection to Byzantine seems to certainly be lost/overlooked. Again, they were a "Greek" nobile family of Bari - so they did have connection to Byzantine, and they did have connection to nobility. And many Emperors used Colaianni as a name. That is my interest !

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For your records (and again, I will gladly email you all of the documents, with digital images of the pages as they appear in the books):
I registri della Cancelleria angioina, ricostruiti da Riccardo Filangieri con la collaborazione degli archivisti napoletani
By Naples (Kingdom). Regia Cancelleria, Riccardo Filangieri
Published by L'Accademia, 1950
The above book lists "Colaianni" as an ambassador of the Paleologo.
Dizionario biografico degli uomini illustri di Terra d'Otranto - refers to
re/King Colaianni throughout the book.
IMPORTANT connection to Byzantine/Paleologo :
1423, Emperor ColaianniThe Basilica of St. Mark in Venice - Giovanni Musolino
- The book reads ,
"IN 1423, Doge Francesco Foscari escorted the
Emperor Colaianni to the top."
If it was in 1423 - it clearly connects to the Paleologo.
Colaianni, Emperor of Trabisonda
St. Andrews University Publications - University of St. Andrews, 1927
"Che Despina, figliuola di Colaianni Imperatore di Trabisonda, Christiana, maritata a Vissuncassano Re di Persia"Storia della Pittura in Italia dal secolo II al secolo XVI.
By Giovanni Battista Cavalcaselle, Joseph Archer Crowe
Colaianni, 1143, Venezia
Colaianni, Byzantine EmperorVenezia nei secoli - Eugenio Miozzi
"Colaianni, Imperatore bizantino - I, 250"
Colaianni, Emperor of ConstantinopleStoria Della Toscana
"Colaianni, Imperatore di Constantinopoli , VI , 188"
Again, these references to Colaianni are all stand alone. The Emperor is referred to as simply Colaianni - so Colaianni was not used simply as a nickname for the first Giovanni.