He made Greek the official language of the state not just called himself Basileus. Which had a big impact on the culture of the empire.
the variance of Christianity that Heraclius championed : For political reasons, as part of his strategy to try and keep the empire together.
More modern Greeks and Turks have descend from the peoples of the Eastern Roman Empire then Germans have from the western Roman Empire. My own surname shows up at least twice in Byzantine sources and I know people whose surname is Metaxas (a family that can trace it's name back to 1000AD and Eastern Rome), Palaiologoi, Comnene, Angelloi e.t.c. and who can track their family histories at least back to the 12th century.
Modern Greek culture is heavily influenced by Byzantine elements (more than Russia or the other Slavic nations) and we also claim that successor status without anybody (except the Russians and Turkey) contesting it.
You know what, I can't make the case as well as others, go ahead and find an english translation (if it exists) of Tomes 7 and 8 of the History of the Greek Nation(Historia tou Hellenikou Ethnous) (ISBN 960-213-095-4, Ekdotiki Athinon, 1980)
It is a pity that no Greek publication house has tried to transalte Paparigopoulos to English, although it makes sense (the series is 8 volumes, each 490-500 pages, so costly). It is the single most important series in arguing for why Modern Greece is one of the spiritual successors of the Eastern Roman Empire.
If you are asking me to summarize the argument here, I apologize but I can't do that, as it would take pages.
And ultimately the argument is less Heraclius did so and so. He was one of many emperors, but he did make Greek the official language. The argument is that Greece (And Turkey to an extent) are successor states of Eastern Rome, for cultural, national, and hisotrical reasons.
Again Paparigopoulos makes the argument better then I do, so if you can find it in English look at it.
As for Iran-> Well I did harp on the Islamic Republic situation which could be an insult. So I do apologize.