Can I make a Group Name for SMS texting?

When texting a group of iPhone users, you can create a name for the group. (This is an annoyingly well-hidden feature; you need to send the group message, then tap the "Details" button at the top by the list of names, then on the next screen swipe the list of names down to reveal the hidden "Group Name" option.)

This seems to be mostly part of iMessage -- I find if I send a group text to mixed platform users, the replies from Apple users stay in the same conversation thread, but replies from Android users come back separately (as SMS messages).

My question is, can I create and save a group of contacts which includes both Android (SMS) and iPhone users?

Related to this, can texts between iPhone and Android users remain threaded together in one conversation?

I tried turning off iMessage but the "Group Name" feature seems vanish along with it. Is Apple flexing its corporate muscles and basically punishing me for having Android using friends, or is there a way to make an SMS group that I am missing?