Name change on passport after lottery selection

I want to go to renew my current passport after selecting in lottery. Main reason to go for renewal is my empty surname on passport and I heard from people that surname empty could create many problems once you reach to US. So I am very confused if I split my name in new passport it would create any problem or not because when I applied for lottery my surname was blank and full name (XXXX YYYY) was coming in given name but if I go for renewal surname would be (YYYY) and given name would be (XXXX).

Please suggest for same,name splitting on passport after lottery selection would cause any problem or it’s fine?

Once you have updated the passport with new name, you need to file H-1 amendment to get the name in the petition updated (I assume petition was applied w/ old name, same as passport). Once that is done, go for H-1 stamping using the amended petition.