The name Asherah in the Bible
Asherah (or אשרות; Asheroth, the plural of Asherah) is the name of a primary Canaanite mother goddess. According to the Oxford Companion to the Bible, she was associated with lions, serpents and sacred trees. In the Bible Asherah is mostly associated with sacred trees or poles (Exodus 34:13, Judges 6:25).
In recent years archeology has revealed that the worship of Asherah was more rampant in Israel than the Bible shows. Initially Asherah was linked to the primary Canaanite male god, Baal (her son) and the evenly prominent Canaanite god El (her mate), but as the cult of Yahweh progressed, Asherah became increasingly associated to Yahweh. Several times the Bible makes mention of an image of Asherah having stood in the temple of Yahweh in Jerusalem (2 Kings 21:7, 23:6).
And not only statues of Asherah made it into the temple of Yahweh, also vessels dedicated to Asherah (2 Kings 23:4) and even facilities for women to weave hangings for her statue (2 Kings 23:7). Statues of Asherah were also erected in Bethel by Jeroboam (2 Kings 23:15) and in Samaria by Ahab (1 Kings 16:33).
Be all that as it may, even though the name Asherah originally denoted a pagan goddess, it's pretty enough and surely well worth being a popular girl's name (like, say, the name Diane, which was a Roman goddess).
Etymology of the name Asherah
The name Asherah comes from the common Hebrew verb אשר (asher), meaning to go straight:
HAW Theological Wordbook of the Old Testament explains that the original name for Asherah had to do with a Ugaritic verb 'tr, which meant the same thing as the Hebrew version Asherah, namely Progression. It's also safe to assume that the original name of this goddess sounded differently (something with a tr-sound no doubt). And that strongly suggest that the original translators of this name wanted to make sure that the meaning of it was conveyed into Hebrew. To any Hebrew audience, therefore, the name Asherah would also have meant Bliss or Happiness; the Semitic equivalent of the Latin deity Fortuna and the Greek Tyche.