From where came the name of Rehoboth Beach, Delaware?

I'm not entirely sure of the process by which the people of Delaware made their decision, but the name comes from another coastal spot in the Bible, in Genesis 26:22. In that verse Isaac names a well by the Mediterranian coast "Rechovot", which comes from the Hebrew root of the word translated as "widening" or "expanding", "for Adonai has expanded our abundance, and we can be prosperous in the land."

This supports Arpeggionist's answer.

The city was founded in 1873 as the Rehoboth Beach Camp Meeting Association by the Rev. Robert W. Todd, of St. Paul's Methodist Episcopal Church of Wilmington, Delaware, as a site for Methodist camp meetings in the spirit of similar resorts on the New Jersey shore, such as Ocean Grove. The Camp Meeting Association disbanded in 1881, and in 1891, the location was incorporated by the Delaware General Assembly as "Henlopen City", shortly after which it was renamed to Rehoboth Beach.
Rehoboth is a name of Biblical appellation, meaning "place [or space] for all". The name is strikingly fitting, due to Rehoboth Beach's ability to blend its distinct communities. Rehoboth appears three times in the Old Testament as, variously, a well dug by Isaac (Wadi er-Ruheibeh) (Gen. 26:22), a city on the Euphrates River (Gen. 36:37; 1 Chr. 1:48), and one of the cities of Asshur (Gen. 10:11). Consequently, the name had obvious appeal to the religious founders of the city.

https://en.wikipedia.org/wiki/Rehoboth_Beach,_Delaware