The conventional wisdom seems to that it means “palm” tree.
True, even if we may be led to believe that it is a Hebrew word in fact it is a word common to several ME languages. At the moment the Arabs use it to mean date, the fruit which we know as “armav” in Armenian. My suspicion is that it it is originally either Assyrian or Aramaic. Why would a girl be named Tamar, I.e. a palm tree?
A palm date may be the sweetest and saccarose fruit of the region. So in fact the name Tamar by inference means “sweet” ...