The primary currency within The Initiative is simply called the "credit".
The credit was first introduced when Sanctuary was first settled. It was conceived as a primarily digital currency, as part of an effort to prevent the need for mints and avoid the drain of resources such institutions would require.
For most exchanges, a person's Identification Chip would serve the same function as a money access card (such as a debit or credit card), removing the ability for pickpockets to gain access to a person's money. A single identification chip could be linked to as many bank accounts as needed. For some transactions, a person could load money onto an actual chip (which would hold the access codes to the money), at almost any terminal. The banking system would deduct the money from the person's bank account, and place it into a special holding account, to later be transferred to whomever would be the eventual recipient of the chip, allowing a complete paper trail and largely removing the ability for criminals to steal funds.
One of the primary shortcomings of the credit is it's highly variable purchasing power, where it's worth may vary from planet to planet, despite being valid across human space.