None, once they made it to England, according to the chronicles. They are sometimes mentioned separately when their immigrations begin, but from then on always together. Some sources will even list the kingdoms founded by the Angles, Saxons, and Jutes (and you thought the Angles were left out) in the British Isles, but again, shortly thereafter they are grouped together. The Latin, too, is sometimes Anglosaxoni. More often than not, everyone is grouped together as "English" after a while. In Old English -- which is what you probably mean by "in Anglo-Saxon" -- the title is Angulseaxan (or some variation of that), but it wasn't used very often and was derived from the Latin term I gave above. More often than anything, sources list the kingdom or territory an individual ruler came from, e.g. Northumbria, East Anglia, Wessex, Mercia, et al. They are referred to together so often because they migrated at the same time over a long period of time. The assimilation and enculturation was not drastic, as with William the Conqueror later, it was gradual. There was also constant conflict between local and regional leaders, leading to a big mishmash of changing borders, which further confused the issue.

You hear about the Saxons probably because Saxony remained a fairly important Germanic duchy throughout the middle ages.

If you want the modern equivalents, look up Angeln and Old Saxony.