Your projects in react-native can't have spaces in them, but you can change the app name directly in the android & ios projects.

For android:

go to android/app/src/main/res/values/string.xml and change app_name to your desired value.

For ios:

Go to ios/[currentName].xcodeproj/project.pbxproj and change the PRODUCT_NAME values, both in debug and release, from the current name to your new name.

or go to ios/[currentName]/info.plist, find this:

CFBundleDisplayName

${PRODUCT_NAME}

and replace the ${PRODUCT_NAME} with your desired name