There are several synonyms for the term "give undertaking", which means to make a promise or commitment to do something. Some common alternatives include "pledge", "commit", "vow", "assure", "guarantee", "swear", "oath", "promise", "undertake", "commitment", "obligation" and "assurance". Depending on the context, different synonyms may be more appropriate. For example, "oath" or "swear" may be more suitable in a legal context, whereas "promise" or "pledge" may be more common in everyday speech. Ultimately, choosing the right synonym can help to convey the desired tone and message of the promise being made.