Adam Clarke on Judges 8:31

His concubine - A lawful but secondary wife, whose children could not inherit.

Whose name he called Abimelech - That is, my father is king, or my father hath reigned. This name was doubtless given by the mother, and so it should be understood here; she wished to raise her son to the supreme government, and therefore gave him a name which might serve to stimulate him to seek that which she hoped he should enjoy in his father's right. See the following chapter, Judges 9 (note).