This question is about philosophy merged inside an historian's perspective.
There is always more than a little risk in interpreting Nietzsche. On my understanding of 'The Genealogy of Morals', genealogy is more than an investigation into origins.
It does involve an inquiry into origins, however. Nietzsche does want to know what has produced morality, what it is that has given rise to it. If Nietzsche were offering merely a myth or speculation to explain the origins of morality, he would not go into so much historical detail. (He is not offering the kind of myth or speculation that Rousseau uses in 'Origins of Inequality' to explain the institution of property and the source of certain social emotions such as vanity and envy.)
His concern with the origins and history of moral values is evident when he talks of the 'need to know about the conditions and circumstances under which the values grew up, developed and changed ... [W]e have neither had this knowledge up till now nor even desired it' (GM, Preface, §6 : Nietzsche, 'On the Genealogy of Morals', tr. C. Diethe, Cambridge : 1997, 8.)
But genealogy means more than this quest for origins. Nietzsche also wants (a) to examine the value of morality as currently understood, to see whether it genuinely contributes to human flourishing :
'So let us give voice to this new demand : we need a critique of moral values, the value of these values should itself, for once, be examined' (GM, Preface, §6: Nietzsche, 'On the Genealogy of Morals', tr. C. Diethe, Cambridge : 1997, 7.)
He also (b) asks what authority morality has. He wants to uproot the idea that morality derives from some supernatural or other authority. We tend to think of moral judgements as truths but we practise a kind of self-deception about their status.
'In practice it means that moral judgments are torn out of the conditionality they grew from and within which alone they make sense, out of their Greek and Greek-political soil, and, under the semblance of sublimation, are denaturalized. The great concepts "good," "just"are severed from the preconditions they belong to, and as "ideas" set free they become the objects of dialectic. One seeks a truth behind them, one takes them as entities or as signs of entities: on e fabricates a world where they are at home, from which they originate [wo sie herkommen ]' (NL 1888: 14 - NL = Nachlass = Notes.
We treat moral values, those we have inherited, as objective and moral judgements as true. Often we see them (or did in Nietzsche's time) as divine commands, as having a supernatural origin. In fact they are just remnants of an older civilisation.
As such they have no authority. We are free to create our own values. This is partly what Nietzsche has in mind when he talks of a 'transvaluation of all values'.
If this is clear, you may now understand why Nietzsche used 'genealogy' of morals instead of 'origins'.
Nietzsche is talking about how morality appears to arise in a succession of changes, each base upon the previous one. He wants to emphasize the organic nature of the succession of moral theories.
He argues that slave morality is formed in reaction to master morality. It can only be understood as a 'second generation' rebelling against its origins.
And ultimately he does not seek an underlying reason for the original master morality. So he is not going all the way back to origins, or even trying to. To that extent, to use such a label would be misleading.