Was Genesis 15:13 given before Abram's name was changed to Abraham?
Yes. Genesis 15:13 was given while he was still called Abram, before his name was changed to Abraham. The verse addresses him as Abram, and the speaker explicitly notes this is before the name change. The promise concerned his seed being strangers in a land not theirs, serving and being afflicted 400 years.
Les explains that Genesis 15:13 records God speaking to Abram, and he points out this is before his name was changed to Abraham. In the verse, God tells Abram to know of a surety that his seed—plural, meaning the whole nation of Israel—would be a stranger in a land not theirs. Les identifies that land as Egypt, where they would serve as slaves and be afflicted 400 years. He notes Exodus 12:40 gives 430 years for the sojourning, showing a later reckoning of the same period.
And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years;