Genesis 32:28 And He said, Your name shall be called no more Jacob [supplanter], but
Israel [contender with God]; for you have contended
and have power with God and with men and have prevailed.
that would be correct.
Exodus 15:22 Then Moses led
Israel from the Red Sea and they went into the Desert of Shur. For three days they traveled in the desert without finding water.
but did Moses lead Jacob/Israel?
Who is Israel??