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Each network still broadcasts its own network code - 234-30 for T-Mobile and 234-33 for Orange. Indeed, the new 4G EE network uses T-Mobile's 234-30 code.

Phones come shipped with a lookup table that maps these codes to network names. The phone can also read this data from the SIM card, thus overriding (but not updating) it's internal data. EE have updated their SIM cards to map both 234-30 and 234-33 to the name "EE", Virgin Mobile have been mapping 234-30 to "Virgin" for a decade, and may now include 234-33 as well, though whether existing customers see that depend on whether their SIM cards are remotely reprogrammable.