More likely Ilija changed his name sometime after he was in the US rather than when he arrived.
Yugoslavia would not exist until after the end of WW I, 1918.
His 1909 ship manifest shows his next of kin at Canak was his mother Marya, which would likely indicate his father had passed.Marya (Marija) lived at 92 Canak.Canak is a long way (77.1 miles SSW of Zagreb) from Zagreb City and Zagreb County, located in the Lika areaHis destination is listed as going to his brother Nikola at 1825 Ohio St, S. Chicago ILCanak is also listed as his birthplace
Where are you finding the placenames Jsigo,Salvio?
The only Nikola CRNJAK I find arrived 1902, DOB c. 1865 destination Chicago IL
On is WW II Draft Registration (called Old Man's Registration) he gave the following info
Name: Eli Cernak Birth Date: 20 Jun 1891 Birth Place: Croatian, Yugoslavia Residence: Chicago, Illinois
Still... a Naturalization record is found with another birthdate Eli Cernak [Ilya Crnjak] 24 Jun 1891 Jugoslavia Illinois, Indiana, Wisconsin, Iowa 18 Mar 1927