I don't think this question applies to Ask historians, where should I ask it?

You could try /r/HistoricalWhatIf

Any answers are likely to be speculative and inconclusive, since I highly doubt the Sauds have a contingency plan in place for renaming the country upon their demise. It could just become 'Arabia', I guess. Maybe something like the 'Republic of Arabia' in a monarchy-overthrowing scenario.