Can I change the occupation listed in my H1B?

I am getting an employer to sponsor me this FY for H1B. Once in US, I want to do:

a. Part time MBA course


b. Appear for Series 3/Series 30 exam to enter the Financial sector

So if I complete either of those and suppose I find a job, will my employer able to change the listed occupation?

Yes, same/different employer can file another petition for you at that time for the new job and you can work for them on it’s basis. You need to be qualified for the offered position.