Currency has always evolved throughout history.
The currency today LOOKS like the currency of the early 1800's, but it has become a 'spreadsheet' currency (most currency today is virtual, it is not in real, physical printed money). It has become debt-based, instead of cash-only. It has become a means of making more money in its own right (interest, for example, on money in bank accounts). It's value is now determined by it's relation to other currencies. Money is exchanged for another currency for profit. It's value is now determined by factors other than it's own physical existence. International banking is now more important to many economies than international trade.
I would suggest that history (the economic collapse of the 'dirty thirties') indicates that actual hard physical currency would once again dominate, over spreadsheet bank-balance currency. The economic model would change. The model would be based on 'present value' instead of 'future potential value'. It would be cash only, 'In God we trust, all others pay cash'. The plastic credit card economy would completely collapse. I can imagine everyone would go bankrupt, all loans and paper money (mortgages, stocks, bonds, bank accounts) would disappear. Huge sums of 'artificial' money would just vaporize. It would be a total reset back to a cash economy from a cashless economy.
But the actual cash, the physical currency, would still continue. People would still trade hard cash for goods, and then exchange that hard cash for other goods. The currency would still have 'value', but it would be real value, not virtual value.
It would be a return to the concept of currency in medieval times - the rich don't have bank accounts, or investments, or stocks, or bonds, they have a roomful of physical currency. 'Investments' would be in tangible products - land ownership, boats, means of production, animals - not money. But exchange would still be done in some form of common 'cash only' currency.
And this physical currency would be much the same as it is today.
The effects on society, and the impact of the economic collapse, would depend on how far the world had evolved into a 'cashless' currency model. The poor, and the marginally employed 'subsistence level' citizen, would see little change. They are pretty much already 'cash only'. But the middle class, whose wealth is now primarily 'cashless' wealth, would see significant impact.
Their wealth would reduce to whatever they had in their wallet.
As to whether there would be multiple currencies or a single surviving currency, it would depend on the extent of global, vs local, trade and travel. If trade was global, it would be done in some globally-based currency. However, if trade reverted back to local economies, then I suggest local currencies would become dominant. In medieval times, it did not make sense to use British currency in Germany, as there were very few opportunities to USE currency earned in Germany and spent in Britain.