Suppose your target variable is attrition. It's a binary variable - 1 refers to customer attrited and 0 refers to active customer. In this case, your desired outcome is 1 in attrition since you need to identify customers who are likely to leave.
Let's say you set 0 as event in the logistic regression.
Logistic Regression Output.
The sign of estimates would be opposite which imply opposite behavior of variables towards target variable (as shown in the image above).
Area under curve (AUC), Concordance and Discordance scores would be exactly same. No change.
Sensitivity and Specificity score would be swapped (see the image below).
No change in Information Value (IV) of variables.