We identify Tell-es Sultan with Jericho because its the ancient settlement on the site of the city called Jericho. The name doesn't come solely from the story of Israelite conquest in the Book of Joshua it was the site of a city in documented history, and is actually still the site of a city called Jericho in the West Bank today.

Tell es-Sultan is also not the only city from the Book of Joshua whose archaeology does not line up with the Biblical account. Tell-el Jezari, Biblical Gezar, follows much of the same pattern. In both cases, there was a sprawling Bronze Age settlement that fell into abandonment and disrepair during the transition to the Iron Age, after which the site only hosted a small settlement, only to see some significant growth around the 8th century before being damaged in the invasions of Mesopotamian conquerors, but the name remained associated with the location all the same. The primary difference between the two (in this comparison) is that Jericho was rebuilt in later centuries.

In the Hasmonean and Herodian periods, Jericho was the site of royal palaces and a town grew up around the royal residence to support it. This town is referenced, still by the name of Jericho in the Gospels on several occasions, and continued to be referenced by that name for the rest of its history.

Now, there is an obvious critique coming: "Just because the city nearby Tell-es Sultan was always called Jericho doesn't mean that Tell-es Sultan was also the city of Jericho." The thing is, it sort of does. Jericho first appears in the book of Joshua, which critical scholars consider part of the Deuteronomistic History. The Deuternomist school of Biblical authors is generally dated to around the 7th century BCE, centered on the reign of Josiah (whose "rediscovery of the Law" in 2 Kings is believed to be the book of Deuteronomy). This means that Jericho was being referenced for the first time in the Bible, when there was a settlement on Tell-es Sultan, likely with ruins of the Bronze Age city still visible in the landscape. This was before the site was destroyed by the Babylonian invasion. Despite that destruction, the site was still known as Jericho when permanent inhabitation was re-established centuries later.

Of course, it is technically possible that the Hasmonean-era Judeans erroneously identified the site with Jericho, but if that is the case, then there is still a historic site, identified in the 7th century with a formidable history, known as Jericho, in roughly the same region of the Jordan Valley as modern Jericho. At some point, the most likely explanation is that the ancient Judahites and their Judean descendants knew that area as "Jericho" and the name stuck.