That is incorrect. The word eternal is associated with religion and god and not 'normal usage' as you construe it.
God is not just 'eternal' though, god implies many, many other things, not least of which is some sense of consciousness.
Reality is certainly a term used in God as ground of being theology.
You know my feelings on theology, however. Misusing or misattributing reality as somehow supporting magical claims validates neither the field nor the claim.
In eastern theologies God is the ultimate reality.
And still something more self-aware, dynamic and involved than just existence. There are theological concepts of an eternal existence within which 'spiritual' rules apply to ideas like reincarnation, Nirvana and one-ness, but those are not 'gods' and where 'gods' are introduced it's with personalities, intentions and awareness.
Your opening statement is thus immedately off the mark considering you have co opted many of the properties of the necessary being from God anyway.
Nothing can be 'co-opted' from gods which don't exist; that something in reality could be eternal is derived from first principles, that someone else mistakenly attributed it to gods doesn't make accepting that it's possibly a necessity 'co-opting' it just means that you got part of your working right.
In view of my accusation I think it would be helpful if you outline, warts and all, your conception of God, bearing in mind I suspect your experience has been largely secular till now.
I'm sure you would find that helpful, it's always helpful when someone actually offers something rather than just sniping from the sidelines. However, in this particular instance I can't really help you, as I don't have a conception of a god, as I've not come across anyone's definition of one which made sense enough to accept.
Firstly if the universe is deterministic then there must be a determiner, whatever it is.
Wrong.
For the necessary, definitially it must be self determining other wise if it is not there is something which determines it and that then becomes the necessary.
Founded on the mistaken first premise.
Since you are saying the universe is determined You have now then almost proved God IMHO.
Except for the failure to understand determinism...
And yet you are suggesting the laws of nature are doing what they do by themselves!!! Oh dear the inevitable cop out by declaration of naturalism.
You realise that's not an argument, right? Why do natural laws need to have been 'selected' by some intelligence, why are they not just an inherent part of the infinite structure of reality?
O.