How should I fill in my name on a visa application if my passport name format differs?

I am applying with Muay Thai soft power at Jakarta embassy. How should I fill in my English and Chinese names? Such as below:

Full name on passport: Anthony Bernard Chan Dak Eng

Machine readable field reads: Chan<<Anthony<Bernard<Dak<Eng

The system populates as:

First Name: Anthony

Middle Name: Bernard Dak Eng

Last Name: Chan

1) Is this correctly filled in?

2) If the visa comes out as "Anthony Bernard Dak Eng Chan", will I have any problems at immigration?

Edited:

The confusion is because the Chinese name is "Chan Dak Eng".

First name: Anthony

Middle name: Bernard

Family name: Chan

Chinese name: Dak Eng

Dak Eng is populated into the middle name field. Is this correct?