Quoting Wikipedia
Avalokiteśvara is a bodhisattva who embodies the compassion of all Buddhas. This bodhisattva is variably depicted, described and is portrayed in different cultures as either female or male.
Thus, the AvalokiteśvarapartAvalokiteśvara part in its name relates to the Bankai's ability to restructure everything into anything.
The key here are the words bolded above. Avalokiteśvara or Kanon, as I would refer to her from this point on, was known in many-many form. But all of those forms are her.
Things have different appearances, called by different names, but they are all formed of atoms, of matter. From the most simple to the most complicated, they are in core are made of matter.
The bankai's ability is to restructure the matter so that one thing becomes another thing. Or if we are to use Kanon, from one appearance of Kanon to another.