What official merchant database exactly?
What Monzo get is a bunch of data that is up to the merchant to set accurately. Often times, terminals move around or get configured with the payment provider incorrectly (everything registered to head office, company names rather than expected brand names used, terminal configuration shared between brands of the same company, etc).
This data also does not always include clean human readable names or logos. For this, Monzo have their own merchant data enrichment service that takes incoming transactions and tries to match them against the database that ties in to various mapping and data sources (though much of it is not used in the app right now, see the API for more).
This merchant enrichment system allows Monzo to know that “DOMINOS PIZZA GROUP MILTON KEYNES GBR” should be displayed as “Domino’s Pizza” with the logo pulled from Twitter or a similar source. That “ITUNES.COM/BILL ITUNES.COM LUX” should be dispalyed as just “iTunes” with the logo and so on.
Even if Monzo has no entry for the merchant, the system will attempt to clean up the names by correcting capitalisation and removing parts such as “PAYPAL *” at the beginning of the raw name provided to them.
On iOS, it is currently possible to submit corrections or changes to these and improve the merchant database by tapping a button at the bottom of the transaction. This feature is not yet available on Android sadly.