Why did the Byzantine record the name of Osman Ghazi as Otoman?

Here’s some data, from Gyula Moravcsik’s Byzantinoturcica, a dictionary of all Turkic names and words that ended up in Byzantine Greek. The names are in roughly chronological order.

Osman is named as:

• Atman (George Pachymeres, Nicephorus Gregoras)
• Atouman Atoumanos Atoumanes (Notitiae Chronicae, Chronicon Turcorum)
• Otmanos Otmanes (Hierax, Chronica Minora)
• Otoumanos (Chalcocondyles)
• Othmanos Othman Otthmanos Otthmanes Otthamanes
• Osouman

From Turkish Atman, Ataman, Azman, Tuman? ~ Arabic Otmān.

So Moravcsik accepts that the name originated as Atman, with abundant bibliography, and the very earliest mentions are as Atman. The versions with an initial O- and with a -th- are 15th and 16th century.