Starshield means multiple things, or really it is SpaceX business unit with military. Starshield is the name for US military buying Starlink service. It is also SpaceX building Starlink-based satellites for the military. This doesn't have to be communications, the first ones were missile defense trackers.

I think the custom satellites came first and they rebranded the communications after it.

That seems entirely plausible. I based my comment on one of Elon's tweets (xeets?) about it: https://x.com/elonmusk/status/2028261823678759335?s=20