Alexandra
Apart from being the feminine version of Alexander, which was the alternate name of Paris, the Prince of Troy who kidnapped Helen and set of a 10-year war, "Alexandra" is one of the oldest attested Indo-European names. Spelled something like "a.la.ksan.da.ra", it is found in the "Linear B" tablets unearthed in Greece. These tablets were written before the destruction of the Greek cities around 1200 BC.
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Yes, but don't forget that Linear B was written in a syllabic script. That means that instead of having symbols for letters, they had symbols for syllables - the fact that it ends in RA probably just indicates that they would have ended it in R if they'd had a loose R available; as it was, the A at the end was neither pronounced nor intended to indicate a feminine form of Alexander.