When "be it" is at the beginning of a sentence, what kind of structure do you call it?

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?

Solution 1:

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.