There are several synonyms that can be used for the phrase "toot own horn". Some of these include boasting, bragging, self-promotion, self-advertisement, self-praise, and self-aggrandizement. These terms all refer to the act of speaking highly of oneself or praising one's own accomplishments. However, it's important to note that while self-promotion may be necessary in certain situations, there's a fine line between confident self-assurance and obnoxious self-aggrandizement. As such, it's best to tread carefully when discussing one's own achievements, and to always remain humble and gracious in the face of success.