This is a general civil agreement. As long as the two sides reach an agreement through consultation and do not violate the law, it is certainly legal and has legal effect. Specifically, the situation you mentioned belongs to the agreement that Party B has obligations, that is, the letter of commitment you mentioned. As long as the personal basic information of the promisor is stated in this letter of commitment, it is the basic information of the unit and legal representative, your personal basic information, the basic information of the event and the liability for breach of contract (the most important thing is to protect your personal basic rights and interests). Of course, if you are not at ease, you can go to the notary office for notarization.