Help Needed- Regarding Name bifurcation

[toddler]

Hello Everyone,

I have a query here:

In my current passport the name mentioned is:
Given Names: ABC XYZ
Surname:this is blank

My employer is filing an H1B for me.I am planning to get my name corrected in the passport as
Given Name: ABC
Surname: XYZ

Wanted to know if I can get this corrected after the H1B lottery takes place and my case is picked up in the lottery.Will I have any issues while filling up rest of the forms or getting the visa stamped because in lottery documents my old passport number will be mentioned and after lottery I will have a new passport.Will this cause any issues later while stamping and all.

Thanks!