The Gemara in Brachot 13a teaches us that we should only refer to Avraham as Avraham and not as Avram.
תני בר קפרא כל הקורא לאברהם אברם עובר בעשה שנאמר (בראשית יז) והיה שמך אברהם רבי אליעזר אומר עובר בלאו שנאמר (בראשית יז) ולא יקרא עוד [את] שמך אברם
Bar Kappara taught: Whoever calls Abraham Abram transgresses a positive precept, since it says, Thy name shall be Abraham. R. Eliezer says: He transgresses a negative command, since it says, Neither shall thy name any more be called Abram.
Does this also apply when the context in which we refer to Avraham is before Avraham was renamed?
For example would we say:
When Avram was born....
or
When Avraham was born....