Ephrath/Ephrathah was indeed later called Bethlehem. But the location of Rachel's death is described as being a distance from Ephrath on the way from Bethel. The term used is כִּבְרָה (Strong's 3530) which is translated variously as anything from a short distance to a long distance or a half-day's journey. Thus the traditional location of her tomb (see map below) may be different from the place she actually died.
A further wrinkle to the problem is added by the way that the term "Ephrathite" is used in the Bible. In addition to being applied to Ruth's mother Naomi and David's father Jesse (both Judahites), it is also used to describe northerners such as the people who could not pronounce "Shibboleth" correctly (Judges 12:5) and Elkanah, the father of Samuel (1 Samuel 1:1). Although the Hebrew term is ephrathi (אֶפְרָתִי - Strong's 673), it is usually translated as Ephraimite. So "Ephrath" may have had a more general meaning than simply the town later known as Bethlehem.
In addition, there was also another town named Bethlehem, quite close to Jesus' home in Nazareth. This has led some modern commentators to conclude that Jesus was actually born in or near the northern town, but a later generation decided that since he was the Messiah, he must have born in the southern Bethlehem. The scriptural basis for the location of a Bethlehem in Zebulon is found in Joshua 19:14 and probably Judges 12:8.
The NT, however, is quite clear that Jesus was born in Bethlehem-Ephrathah in Judah (not further north) because this fulfills the prophecy of Micah 5:1:
Micah 5:1
But you, Bethlehem-Ephrathah least among the clans of Judah, From you
shall come forth for me one who is to be ruler in Israel; Whose origin
is from of old, from ancient times.
Conclusion: In the end we are left with a quandary. The NT clearly sees Bethlehem/Ephrath as referring to Bethlehem of Judah, based on the prophecy of Micah. But there was also a Bethlehem in Galilee. Moreover, the term Ephrathite is sometimes used in the Bible to mean Ephraimite. However, to stick to the OP's question, the place where Rachel died seems to have been located at place further north than her traditional tomb.