The name sequence simply follows what is in the machine readable part of the passport. Which is Last followed by First/Middle. I would say not to worry about the sequence since the app is reading it from the passport.
As for group name, i believe that is just for the app and it makes it easy for you to fill in future arrival cards by retrieving the same group. So you can name it whatever you want.
If you use the website version of the arrival card, it doesnt ask for a group name. You just add all the people traveling together and submit.
https://eservices.ica.gov.sg/sgarrivalcard/