From Namespedia - Names Meaning and Origins
The surname “Kresha” seems to be found only in the United States, starting in the 1870's. It can be traced it back to Theodor Kressa, House #33 in what is now Nova Hradecna, Czech Republic.
Several of his children, Theordor,Jr, Adolf, and Joseph emigrated to the United States in the 1870's to avoid being conscripted into the Austrian Emperor Franz Joseph's "School Boy Army" at age 15. When four of the children landed at Liberty Island in September 1888, they gave the name Kressa. Problem is that the letter /s/ is pronounced /sh/ in English. It came out Kresha. Being young and not wanting or being able to afford to go back, they accepted this spelling and went on.
For further information, please check kreshafamily.com, a website I am developing for the families.