Someone has published a book filled with questions asked of Rav Chaim Kanievsky and his answers.

In the book, an interesting question posed to Rav Kanievsky is if someone cannot get his children into his school of choice because he is Sefardi with an obviously sefardic name, would he be allowed to change his name ot an Ashkenazi name or would that be considered deceitful?

Rav Kanievsky answered that if he knows he can get his kid into the school and the only impediment is the name, it is not considered deceit, as the main thing is to get the kid into the school.
source: Kikar

It kind of leaves things open - is anything to lie about and change, as the main thing is to get your kid into school?

And why is the main thing to get your kid into this specific school? Why not a different school?

I remember hearing similar piskei halacha from rabbonim about the allowance to lie on school application forms denying you have a computer with Internet, or way back when that you had a television. The justification was "for chinuch it is ok to lie". Obviously that needs some qualifications, as lying is not usually good chinuch, and surely sometimes lying must not be ok even for chinuch. Changing your name isn't lying, but it is creating an at least false impression. It might not be as bad as actual lying, as sometimes the principle of these schools know the people are changing their names, and they are ok with that - they just don't want the Sefardi-sounding names in the school.