What did she beg me not to do?

The choice "To tell anyone I had seen her" is the correct transformation because it maintains the original meaning of the request made. When someone begs you not to do something, they are typically expressing a strong desire for you to keep information confidential or to avoid a certain action. In this case, the phrasing conveys that she specifically pleaded with you to keep it a secret that you had encountered her, which aligns with the nature of begging not to disclose specifics about their whereabouts or condition.

The other options might involve different nuances or implications. For example, begging someone "not to forget her name" or "not to leave without saying goodbye" reflects different types of requests that pertain to personal interactions or emotional connections, which diverts from the idea of confidentiality. Similarly, "to mention her to others" suggests a broader context of communication that could include casual conversation rather than the focused secrecy indicated in the correct choice. Thus, "To tell anyone I had seen her" captures the essence of the plea to maintain privacy surrounding the encounter.