‘Wherefore he called that place Beersheba, when there they swore, both of them.' Beersheba means ‘the well of seven', and is the name given to that particular well. The name is given to remind both sides of the treaty that has been made about it, sealed by the giving of the seven ewe lambs.
Genesis 21:14 refers to the wilderness of Beersheba. It could be that Abraham takes the well known name of the wilderness and applies it to the well because it is appropriate. Alternately it may be that the wilderness originally had another name, altered to Beersheba when Beersheba became well known, for the name Beersheba is eventually applied to a city. (Genesis 26:33 refers to a city of Beersheba, whose name appeared subsequently to that time, and that is the general meaning of Beersheba later on).