be.zeq is a proper place-name used for a muster and for fighting in the accounts cited.

The attested proper-noun use identifies a location: a muster occurs there in 1 Samuel 11:8, while Judges 1:4 and Judges 1:5 place Judah's fighting there.

1. Place named in muster and battle scenes · dominant

   All three occurrences are tagged Noun · Proper. In 1 Samuel 11:8 the APB renders a muster "at Bezek"; in Judges 1:4 and Judges 1:5 it renders fighting and striking "at Bezek" and "in Bezek."

   1 Samuel 11:8Judges 1:4Judges 1:5

In the Anselm Project Bible: The APB presents the name directly as "Bezek" in each verse, using "at Bezek" in 1 Samuel 11:8 and Judges 1:4 and "in Bezek" in Judges 1:5. These prepositions reflect the clauses rather than a separate meaning of the name.