Ethno-nationalist identities in Early Medieval England are a contentious topic. The English themselves never really call themselves Anglo-Saxon; the closest we get is a brief period in the late 9th and early 10th Centuries when Alfred and Edward occasionally adopt the clumsy title Rex Anglorum et Saxonum in the politically messy decades where Wessex is expanding aggressively into 'Danelaw' East Anglia and increasingly attempting to exert authority over Mercia. But even then, as you've noticed, the Jutes are still conspicuously absent.

The idea that the English arrived in discrete national groups and settled in clearly delineated areas giving rise to explicit Angle, Saxon and Jutish ethno-nationalities within 'England' is one that really crops up with Bede in the 7th Century, and one that doesn't really match up with what happened in the preceding centuries. The arrival and integration of the English into sub-Roman Britannia seems to have been a piecemeal affair that differed greatly based on location between quiet integration into existing communities, assumptions of elite roles in extant kingdoms, violent annexation, and simply founding new communties in land left vacant. This leaves a patchwork of, essentially, small 'tribal' kingdoms which may or may not have overlapped with pre-existing sub-Roman, or indeed resurgent pre-Roman, British identities. Kingdoms like the Waeclingas in Hertfordshire, or the Magonsaete and Hwicce along the Severn. It's only as some of these kingdoms expand and seek to consolidate their power that we see Bede's ethno-nationalist identities arising: a 'West Saxon' kingdom stretching from Devon to Hampshire, an 'Anglian' Northumbria, a unified Kingdom of the East Angles stretching from Essex to Norfolk.

These identities assigned by Bede don't always play out in action, and that's what seems to have happened to the Jutes. In Mercia, for example, the "Anglian" identity prescribed by Bede doesn't really seem to figure. Rather than the centralised hereditary monarchy of kingdoms like Wessex, the Mercian leadership seems to have been a form of tribal hegemony, with kingship rotating between a small number of clans in what was, essentially a 'federated' system. Although the Welsh refer to them as Anglii - perhaps from Bede - the political nomenclature adopted in Mercia itself therefore was one curiously devoid of such sweeping ethnic groups. The Mercians were just that; Mercians, although sub-Mercian identities such as the Hwicce and the Magonsaete persist in the attestations of charters.

According to Bede, the Jutes largely settle in Kent. The Kingdom of Kent provides us with our earliest written English sources, as Augustine's mission of 597 arrived first in Canterbury. What those sources, and indeed the names Kent and Canterbury, tell us is that the Jutes who arrive in Kent, if indeed they identified as Jutes, integrated themselves into extant pre-Roman communties rather than conquering themselves a kingdom of their own. In legal codes and charters, the 6th and 7th century kings of Kent identity themselves as Kynges Cantwaras, or Kings of the people of Cantiaca, the Brythonic/Roman name for the area. It's likely that these were some of the first established and most thoroughly integrated of the foederati which comprised the first wave of English settlement, so it's curious as to how much 'Jutish' identity they would have espoused as late as the 7th Century. Certainly by the 9th Century, Kent had been a subkingdom of first Mercia and then Wessex for some centuries, so is likely to simply have been considered "Saxon" for the purposes of the Rex Anglorum et Saxonum.

To my knowledge, the three Germanic tribes that invaded England after the fall of Rome were the Angles, the Jutes and the Saxons. Why are the Jutes not in the name "Anglo-Saxon"?

The term "Anglo-Saxon" was introduced by medieval scribes, who used it to differentiate between "the English" as they existed in their time and English society prior to the Norman invasion under William the Conqueror. It literally means "English Saxons" as opposed to the "German Saxons" living in the then existing Duchy of Saxony. It fell out of use after a few centuries, only to be revived by 16th and 17th century English Humanists to refer to the language now generally called "Old English".

Modern historians use it in the following sense, to refer to the Germanic-centered culture of Britain that existed between the Roman withdrawal and the Norman Conquest. "Anglo-Saxons", in this regard, are people belonging to this cultural group, but it was never used by the people we now know as the "Anglo-Saxons" to refer to themselves during the Migration Period or Early Middle Ages. As an ethnic term, none of the Germanic speaking groups then present in what is now Britain referred to themselves as "Anglo-Saxons". The actual "Anglo-Saxons" referred to themselves in various ways. The so-called Tribal Hidage (compiled somewhere around 750-850) lists some 35 different tribes. Some of these are familiar, such as the East Angles and the Western Saxons, but others, such as the Herefinna or Unecungaga, are unknown from any other source and remain obscure today.

Most of the terminology surrounding the Anglo-Saxons, comes from people who were not Anglo-Saxons themselves or lived much later in term. For example, Gildas refers to all of them as "Saxons", Procopius speaks of Anglii, Frissones and Brittones, whereas Bede (himself probably an Anglo-Saxon) was the first to provide the now familiar dichotomy; dividing these immigrants into Jutes, Saxons or Angles in his Historia ecclesiastica gentis Anglorum.

Bede more or less caused of your question, because traditional 19th century historiography (and by extension the popular consciousness) has, essentially, never stopped repeating his tri-partition of the Germanic people that "invaded" Britain. That's how, in the popular mind, "Anglo-Saxons" became linked to "Angles, Saxons and Jutes", being perceived as shorthand for "Angles, Saxons and Jutes" when in reality "Anglo-Saxon" really is a blanket term for a much broader cultural horizon rather than a specific ethnicity or set of ethnic groups.

Apart from all that, the idea of clear cut tribes like the Angles, Jutes and Saxons invading the British Isles, is considered to be far too simplistic and inaccurate by modern historians. What has been called the Anglo-Saxon invasion, was in reality a long period of immigration of Germanic-speaking groups to Britain, some of these migrations began quite some time before the fall of Rome. Most of these immigrants, spoke North Sea Germanic dialects and had previously lived near the North Sea coast and initially adhered to various forms of Germanic paganism.

As for to which tribes they belonged, there is no evidence at all for a full tribal migration. Historical and archaeological evidence suggest the Germanic settlers moved in family groups, extended families or (at most) clans. It's unclear to which extent the names for these people are based on older Roman geographical/historical works or the actual autonyms.

For example, it has been conclusively proven that the people who are today called the "Frisians" do not descend from the Frisii and Frisiavones of Roman times, but were instead given their modern name by Frankish chroniclers (writing in Latin) who kept using older geographical and tribal nomenclature. Given that these 6th century "Frisians" immigrated to the Northern Netherlands from the exact same area as the Germanic settlers of Britain (indeed, it has been suggested that these "Frisians" were actually the bulk of the migrating "Jutes" of Northern Denmark) it is possible that the "Saxons" were named in a similar way, for example due to the presence of the already existing "Saxon Shore / litus Saxonicum ".