Thanks for all the replies.
@Rovertek - in terms of what the visitor sees H2 is fine for this but in terms of what Google sees H1 is more important. So this is an SEO question.
@kryten - comprehensive answer, only thing is, I’m using RW to avoid getting into code at all! I’ve also been caught out in the past when I’ve switched themes and lost (forgotten) modifications I’ve made.
@teefers @robbeattie looks like this is the work around, not great 'cos overriding the site anything stores up problems down the line when you do want to make a site wide change.
And agree, its a shame the Split theme (and probably others) assume site title is an H1, that is going to hit a lot of sites that want to be search engine friendly.