[Burrow] suggests that Saraswati was a proto-Indoaryan term, originally applied to the present Haraxvaiti when the proto-Indoaryans still lived in no… - George Erdosy

As for Burrow‘s thesis that some place names reflect the names of geographical features to the west, and thus preserve an ancestral home, they once again rather rely on an assumption of Arya migrations than prove it. [...] His cited equivalence of Sanskrit Saraswati and Avestan Haraxvaiti is a case in point. Burrow accepts that it is the latter term that is borrowed, undergoing the usual change of s- > h in the process, but suggests that Saraswati was a proto-Indoaryan term, originally applied to the present Haraxvaiti when the proto-Indoaryans still lived in northeastern Iran, then it was brought into India at the time of the migrations, while its original bearer had its name modified by the speakers of Avestan who assumed control of the areas vacated by proto-Indoaryans. It would be just as plausible to assume that Saraswati was a Sanskrit term indigenous to India and was later imported by the speakers of Avestan into Iran. The fact that the Zend Avesta is aware of areas outside the Iranian plateau while the Rigveda is ignorant of anything west of the Indus basin would certainly support such an assertion.

The idea has recently been challenged by archaeologists, who ― along with linguists ― are best qualified to evaluate its validity. Lack of convincing material (or osteological) traces left behind by the incoming Indo-Aryan speakers, the possibility of explaining cultural change without reference to external factors and ― above all ― an altered world-view (Shaffer 1984) have all contributed to a questioning of assumptions long taken for granted and buttressed by the accumulated weight of two centuries of scholarship....

We reiterate that there is no indication in the Rigveda of the Arya‘s memory of any ancestral home, and by extension, of migrations. Given the pains taken to create a distinct identity for themselves, it would be surprising if the Aryas neglected such an obvious emotive bond in reinforcing their group cohesion. Thus their silence on the subject of migrations is taken here to indicate that by the time of composition of the Rigveda, any memory of migrations, should they have taken place at all, had been erased from their consciousness.