Do I have to include thesis topic/advisor name after career change? Here is a related question but not exactly what I'm looking for

Should one include irrelevant background on CV after career change?

My Scenario:

I dropped out from a Ph.D. program in [subject X] and got a M.S. in [subject X]. One of the M.S. requirements was a thesis. My relation with my former advisor was horrible because of [a long story of advisor-advisee confrontation]. I do not want anyone asking his opinions about me.

I'm currently a Ph.D. student in [subject Y] and I want to construct a CV for the purpose of personal academic website under my current department.

In my education section of CV, can I omit the name of my advisor/thesis topic? For example,

[time] M.S. in [subject X] [name of University]

instead of

[time] M.S. in [subject X] [name of University]
Advisor: [Name of Advisor]
Thesis: [Topic of Thesis]

In the future, if I end up in getting a Ph.D. in [subject Y] and picking up master along the way. Can I completely remove everything related to [subject X] on my CV that is used to apply for postdoc. position in [subject Y]?
You are not obliged to include any information in your CV, IMHO, neither morally nor legally.

Of course, people can be asking what were you doing if you got your masters (let's say) in 2012 and started your current PhD programme in 2015, and they'll likely ask you in an interview about this. Or (especially if there are no interviews, which is the case for many PostDoc programmes) simply not consider your application because of the "grey areas".

As for whether to do this or that: Remember that in academia, CVs are very verbose and usually contain all relevant information. If you're deep into your current PhD and you have some publications, I don't think that listing details on your masters is necessary. I, for one, do not list the names of the supervisors at all; they are obvious from my publication record.