The name Asher in the Bible
There are one man and one town named Asher in the Bible. Asher the town was situated on the southern border of the territory of Manasseh (Joshua 17:7). Asher the man was Jacob's son number eight and his second one with Zilpah (Genesis 30:12-13).
Asher's only full brother was Gad (Genesis 30:9-11), and Asher's sons were Imnah, Ishvah, Ishvi and Beriah. His daughter was named Serah (Genesis 46:17). Asher's descendants, the אשרי (Asherites; Judges 1:32) would form one of the twelve tribes of Israel and settle the northern portion of Israel's Mediterranean coast.
In Greek this name is spelled Ασηρ; Aser (Luke 2:36, Revelation 7:6). The name Asher should not be confused with the name Asshur, although these names appear to be quite kindred. In fact, the name Asher may come from a deity of that same name, which also lent its name to the Assyrians.
Etymology of the name Asher
The name Asher comes from the Hebrew verb אשר (ashar) meaning to go (straight) on:
And apparently, the Canaanites found progressing so pleasing even that they adored a goddess with the feminine variant of this name: אשרה (Asherah, 1 Kings 15:13), often referred to by the plural אשרות (Asheroth, Judges 3:7).
For a meaning of the name Asher, Jones' Dictionary of Old Testament Proper Names and NOBSE Study Bible Name List both read Happy.