Today when we talk about Germanic mythology we invariably use the Old Norse names for mythical figures and places. But it's known that the same mythology was held (more or less) in common by all Germanic peoples, including the English (as evidenced by the names of the days of the week), so what would the English names have been for, let's say, Odin, Thor, Loki, Ymir and so on?
Well we are at a strong disadvantage when it comes to examining Anglo-Saxon pre-Christian beliefs compared to the much more thoroughly attested examples from Scandinavia. There was never an equivalent to the Icelandic sagas written in Anglo-Saxon England. The few sources that do trace their lineage back to pagan times have still come about in a Christian context. While they are not totally scrubbed clean of references to pagan deities and figures, Weland the smith for example features in Norse sagas, Beowulf, and perhaps in a depiction on the Frank's Casket, there are no literary accounts drawing upon an extensive pagan tradition. Even in these sources, Christian influence is quite palpable in many places. Because we lack a "canon"of Anglo-Saxon pagan work, even if the sagas shouldn't necessarily be held to such a strict standard, it is really impossible to construct a full pantheon with clear parallels to the famous Norse examples.
We do have some sources available to us that can also help clue us into the names of their deities through place name studies. While still somewhat rare in England compared to Scandinavia, places bearing the names of Germanic deities are far from unheard of. A full accounting of all these places is a little beyond the scope of this question, but by far Woden is the most common deity to be used in place names, with Þunor and Tiw also having a few, and a smattering of other places have also been attribute to deities such as Frig and Frey. Also the literary record is not totally absent of any references to pagan deities. There is a surviving incantation/medical text that invokes the name of Woden directly.
Our names for the days of the week are actually pretty useful here, since they've retained their pagan namesakes pretty clearly, even if Anglo-Saxon pagans would not have had standardized names to refer to them always as. For example, Woden, Wodnes, and Wednes are seen in various place names, and while all clearly related, there was never one universal spelling. Tiw, Þunor, Woden, and Frig are all present in days of the name of the week. I'll admit I am unsure what the consensus is on Monday and Sunday and whether they are referring to deities or to the celestial objects, or both.
So to bring this back around to your original question, what would the Anglo-Saxon names be for detieis/figures such as Loki or Ymir? We quite simply don't know if they even figured into Anglo-Saxon mythology to begin with. All we are left is essentially the bare bones of Anglo-Saxon pagan deities.