Русско-англо-русский юридический словарь

On Friday, March 21st, 2014, L'Oréal and Nestlé signed the share purchase agreement; the completion of the sale is conditional upon the approval of the sale by the competition authorities. (Reuters)

In some common law nations, a recognizance is a conditional obligation undertaken by a person before a court. It is an obligation of record, entered into before a court or magistrate duly authorized, whereby the party bound acknowledges (recognizes) that they owe a personal debt to the state. A recognizance is subject to a "defeasance"; that is, the obligation will be avoided if person bound does some particular act, such as appearing in court on a particular day, or keeping the peace. The concept of a recognizance exists in Scotland, Hong Kong, Canada and the United States. People who are released on their own recognizance are subject to appearing before a judge on a certain day in the near future. (Wikipedia)

Conditional Acceptance A conditional acceptance, sometimes called a qualified acceptance, occurs when a person to whom an offer has been made tells the offeror that he or she is willing to agree to the offer provided that some changes are made in its terms or that some condition or event occurs. This type of acceptance operates as a counteroffer. A counteroffer must be accepted by the original offeror before a contract can be established between the parties. (West's Encyclopedia of American Law)

In everyday use "in the name of" is taken to mean that you are invoking the full authority of someone or something else such as an official, or the law, or even of God but "on behalf of" is taken to mean that you are acting as an agent of someone else with only limited or conditional authority. (EnglishForward)