As others have said, we think of the egg as being made up of the shell, the white (albumen) and the yolk.
You aren't thinking of the colourless or whitish strand in the albumen, are you? This is called the chalaza (plural: chalazae), but not many people use the term. This is the chord that connects up the yolk to the shell. If you break open an egg, it looks like this:
I agree it is the white of an egg. It is often called an "egg white". A cooking recipe might say "Use 4 egg whites for the chiffon. Save the 4 yolks: we will use them later."
If you break the yolk and mix it thoroughly with the white, it is called "scrambling the egg". "Scrambled eggs" (cooked on a grill) is a common breakfast dish. "Fried eggs" are eggs cooked on a grill without scrambling: the yolk is not broken.