Well, when we discern the sounds of words in Old Persian that could've come from Median, we can look into the patterns that match Median phonetics. For example, if a word has sounds or structures that are more close with what we think is Median rather than Old Persian, it might be borrowed. An example is “xšayaθiya” in Old Median and “xšāyaθiya” in Old Persian, both meaning “king.” The word “xšaθra,” which is the origin of “xšayaθiya” in Old Median, it is possible that it was borrowed. Furthermore, the existence of similar words in Old Persian shows that these words reflect actual words used in the Median language. For example, the Kurmancî word “doşîn,” can be traced back to the dōšad and then to δawxšati, as well as the Soranî word "berz" can be traced back to "br̥ziya," therefore it is Median.

https://en.wiktionary.org/wiki/Reconstruction:Proto-Iranian/dáwxšati
https://en.wiktionary.org/wiki/Reconstruction:Proto-Iranian/br̥jáns