Short answer (as JoelK noted, see this one for more) -- disagreement among grammarians about cases like this. Listen to your favorite baal kriah read Exodus 7:29, about the frogs:
וּבְכָה וּבְעַמְּךָ, וּבְכָל-עֲבָדֶיךָ
All three of those "vet"s are in that same gray zone.
As it was taught to me -- you can't start a word with two sh'vas, as you'd ...
I think the answer may be that it goes back to terms used in the Chumash. Rosh Hashana comes from the verse
אֶ֕רֶץ אֲשֶׁר־יְהוָ֥ה אֱלֹהֶ֖יךָ דֹּרֵ֣שׁ אֹתָ֑הּ תָּמִ֗יד עֵינֵ֨י יְהוָ֤ה אֱלֹהֶ֙יךָ֙ בָּ֔הּ מֵֽרֵשִׁית֙ הַשָּׁנָ֔ה וְעַ֖ד אַחֲרִ֥ית שָׁנָֽה
and Rosh Chodesh comes from the verse
הַחֹ֧דֶשׁ הַזֶּ֛ה לָכֶ֖ם רֹ֣אשׁ חֳדָשִׁ֑ים רִאשׁ֥וֹן הוּא֙ לָכֶ֔ם ...
I think part of the question is your statement "is called". I am cobbling together some thoughts with no real authority so I apologize, but I think it difficult to account for conveniences and popular trends that might not have any halachic weight.
The first thing is that there are contexts in which the noun has no introductory definite article -- ...