Visa won’t be a problem for you. An applicant for a student visa only has to submit documents that prove they have been admitted to a university in the country they are applying for the visa to. Since you haven’t received an admit yet, you would have to ensure that the name on your university documents is the same as your legal name on your passport.
Thus, it completely depends on the institutions you’re applying to.
There are two ways to go about this.
1. If you haven’t submitted your MBA applications yet
The GMAC allows applicants to change their names on the test. this can be done for various reasons including a legal change of name. However, once you get your name changed on your MBA.com account, you will have to buy new score reports and send them to the schools you wish to apply to.
It’s more complicated for the IELTS though. IELTS doesn’t allow you to change your name on an existing score report. Thus, you might have to take a fresh test with your changed name if a school insists on having the same name on your IELTS score-card as the one on your passport.
2. If you have already submitted your MBA applications
The business school you have applied to must have a policy regarding the name discrepancy from your business school application to your official score reports. Simply contacting the admin of the schools you have applied to can help you with the policies regarding the same.
While some schools might allow you to simply submit your legal application regarding the changed name, others would require the score reports with your new name. In the case of the latter, follow the same process as point 1.