May I suggest "Hellen Hegemony" or "Hegemony of the Hellenes" instead of "Empire of the Hellenes"? Since they always intitle themselves Hegemon, it sounds more flavourful.
Also, for a hypothetical "Empire of Saxon Britain", I suggest a long-lost form of Old English idiom: Kingrike / Kingrick, or Cyngerice. It contains the old Germanic root for "rule, authority" that developed the German "Reich". I think that, in this alternate Saxon Britain, "Reik" or "Rike" can become a similar concept. Several "kingdoms" inside one single "kingrike". Thus, this empire level title would be something like "Kingrick / Kingrike of Britain".
Or Bretwalda, the Ruler of all Britain.
Also, for a hypothetical "Empire of Saxon Britain", I suggest a long-lost form of Old English idiom: Kingrike / Kingrick, or Cyngerice. It contains the old Germanic root for "rule, authority" that developed the German "Reich". I think that, in this alternate Saxon Britain, "Reik" or "Rike" can become a similar concept. Several "kingdoms" inside one single "kingrike". Thus, this empire level title would be something like "Kingrick / Kingrike of Britain".
Or Bretwalda, the Ruler of all Britain.