By what name was Sebastian first known to Antonio?
Sebastian was first known to Antonio as "Roderigo."
To provide some context: Antonio is the sailor who rescues Sebastian (Viola's twin, who she presumed dead) from the shipwreck at the beginning of the play. Sebastian and Antonio immediately become friends (and in some interpretations of the text, they are also lovers); in fact, according to Antonio the pair are together for the entirety of the three months that have passed since the shipwreck:
No interim, not a minute's vacancy,
Both day and night did we keep company.
Despite their close personal relationship, Sebastian has been lying to Antonio and calling himself Roderigo instead of revealing his true identity as Sebastian, son of Sebastian of Messaline, who Antonio would have heard of. It is not until Sebastian decides to leave behind Antonio and seek out the court of Count Orsino that Sebastian tells Antonio his true name. Despite this deception and the dangers that Orsino's court pose to him, Antonio longs to keep Sebastian's company, claiming:
But, come what may, I do adore thee so
That danger shall seem sport, and I will go.