It is not an old phenomenon.
The current circulation coins of Bangladesh has higher denomination showing Bank's name.
The coins issued by country are accounted for by finance ministry, in government budget as money.
The currency notes and coins with banks name, are promissory notes or metallic equivalent thereof.
Bangladesh Govt. is currently authorised to issue coins only up to 2 Taka.
And are there still any private authorities, rather than public ones, that issue the national coinage in some countries?
Hong Kong notes are issued by three banks, one of which is Standard Chartered Bank, listed in London and Hong Kong Stock exchanges. If ever, Hong Kong decides to issue coins above 10 Dollar face value, it might be issued by these banks, if the current law is not amended.