Hello, SpiderJon, and welcome to the Grammar Exchange.
Which of the following is correct (or more correct)?
1. "How would you like your name included in the minutes?"
2. "How would you like your name including in the minutes?"
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?