Most of the countries in the region do correspond relatively closely to one or a few Ottoman provinces, and in many cases to even older regional identities. Sure, it's not the same as countries which have been actually independent for centuries, but as an inhabitant of a country that had a clearly defined local identity many centuries before becoming actually independent, I can tell you full independence isn't a requirement to develop a national identity. And in the seventy-ish years since their actual independence, most of these countries have focused very strongly on promoting nationalism. Some minority groups may reject that national identity, but that's no different from Catholic Republicans in Northern Ireland, Basques and Catalans in Spain, etc.
As for clans - for a sizeable part of the population, yes, but far from all. The Bedouins and some rural groups in Iraq, Jordan, I guess also Syria, even in Israel, are indeed still to a large extent sticking to their old clan structures, but there are also other regions and the major cities where clans haven't played an important role for centuries.
And I think Cannoli said it pretty well re: 'Arab world'. It's hardly a misnomer. You might as well say the name 'Russia' should be used only for the European part of the country, if you're going to start like that - and those conquests were obviously much, much more recent than the Arab ones.