@Gustavo, Co-Moderator posted:
Hello, SpiderJon, and welcome to the Grammar Exchange.
The only sentence that is correct is (1), as it is short for a passive infinitive.
As you know, "would like" is always followed by an infinitive. The question in the active voice would be:
1'. How would you like me / us to include your name in the minutes?
In the passive voice, "your name" becomes the subject of "to be included," and "to be" can be omitted:
1. How would you like your name (to be) included in the minutes?
Many thanks for such a swift explanation.