Were the first and third person singular forms of verb earlier the same?

Question

I've read Lord's Prayer in German (Vaterunser) recently and found an intersting thing.

Where the third person signular form of the verb is supposed to be used, we see the first one:

Vater unser im Himmel, geheiligt werde dein Name.

Dein Reich komme.

Dein Wille geschehe, wie im Himmel, so auf Erden.

My question is, were these forms in the past the same? If yes, why have they changed (werde → wird, komme → kommt, geschehe → geschieht, and so on)?

Update. I'm not native English speaker, so the comparison with English version doesn't explain me, why it is so. But with Ansgar Esztermann's answer, I finally got it! Thanks.

Answer 1

Like @Em1 said, this is the subjunctive form. Cf. the English version:

Holy be Thy name

Thy kingdom come

Thy will be done

That is, this is not supposed to be statement of facts, but of wishes.