How was Trinity introduced to The Matrix?!
Question: Did she have a name at one time, or anything?
Answers: Did she have a name at one time, or anything?
She was introduced just like every other human on the planet. She was born in an incubation chamber, and hooked into the system as an infant. That was part of the truce in the war with the machines.
If you meant, how was she awakened, most likely Morpheus found her.
Her real name is unknown, though she was an accountant.