The hamitic race is a fake psuedo-scientific concept popularised by american white men in the 1800s when they compared the east-african and nort africans and saw similiarities. Cushitic is a language group in the greater afro-asiatic language familiy like berber, chadic and semetic. Cushitic should not be mistaken for ethnic corelation even though it is often so. We see other cushitic speaking peoples like beja, oromo anfar and they all have many of the same elemenets culturally, lingustically, geographical and we share much of our dna and phenotype in some ways. The semetic speaking eastaficans are also in the same group because they got a linguistic and cultural shift when they intermingled with the yemeni. Cushitic should also not be compared to the kingdom of kush in the bible or the ancient kingdom of kush in modern sudan.
Somalis don't share much genetic similarities with the modern day arab man. But he have some north african elements and some small fraction middleestern. But over 30 percent of our ancient dna comes from the levant from the ancestors of the arabs some 15 thousand years ago, so it would not be accurate to say we are part arab we are like equal cousins that drifted appart in long time and went through many changes and mutations. Our east african dna is actually so uniqe, the dna test can't compare it too other peoples.
North africans, east africans and middleeastern has gone through too many changes to be called one people. We are not the same. But we share many things lingustically. The afro-asiatic actually came from east africa and became semetic, egyptian, chadic, bereber and hebrew. We are not a byroduct of them, but they adopted elemtents from us.
People in east africa share linguistics, genes and geography, so "East african" would be more correct name to go by.