It is known as the ‘balance sheet’ because it is a fundamental accounting truth that the total value of the assets of the business is equal to the total value of the claims that others have over those assets. i.e. the business itself owns nothing and it only has control of assets that are actually provided by others and which are ultimately owned by them.
This truth is represented by the accounting equation which is also the basis of the structure of the ‘balance sheet’ report:
So in accounting there is always a perfect balance between the value of the assets of a business and the claims by others over those same assets. The financial statement that demonstrates this relationship is known as the ‘Balance Sheet’ or more recently it has become known as “The Statement of Financial Position”.