I think it is kind of inversion and I'd found some info on Wikipedia, but I cannot recall what term this structure is, I even remember some examples from Wiki, say, "be it ever so humble, there's no place like home." Can anybody help me out?
In terms of morphology, the verb is in the subjunctive mood (be rather than indicative is).
In terms of word order, we’re dealing with a case of subject-auxiliary inversion (be before the subject).
In terms of semantics, the structure can express a variety of meanings such as optative, a wish or a hope (be it the best year of your life), in which case the structure carries archaic, formal, often religious connotations. But in your case it encodes arbitrariness or free-choice, ‘no matter which’ (be it new or be it old), or concession, ‘although, even if, even if I grant’ (be it as it may). The two uses are difficult to distinguish.
So your construction could be described quite well as a case of subject-auxiliary inversion with free-choice/concessive, subjunctive be.