Towards Better Davening and Torah Reading
It is fairly well-known that if one begins a bracha, and says BARUCH ATA HASHEM, and then realizes that the bracha should not be said, he/she may "prevent" G-d's name from being said in vain by quickly adding the words LAMDEINI CHUKECHA, thus completing a pasuk in Tanach, spcifically T'hilim 119:12.

BARUCH ATA HASHEM LAMDENI CHUKECHA:
Reciting a pasuk in Tanach with G-d's name in it is NOT considered taking His name in vain, so the quick adding of the last two words in the pasuk "does the trick".

If one got to the next word before realizing that the bracha should not be said - BARUCH ATA HASHEM ELOKEINU - then here is what one source (quoted in EIM LAMIKRA HASHALEIM) suggests. Say the rest of D'varim 5:2 (this week's sedra, which is why we are looking at this topic in the first place):
HASHEM ELOKEINU KA'RAT I'MANU BRIT B'CHOREV:
Having said HASHEM ELOKEINU in vain, adding the words KARAT IMANU B'RIT B'CHOREIV finishes off a pasuk in Torah, which "saves" the names from being in vain. The words one started with in this case - BARUCH and ATA - are ignored.

The two words HASHEM ELOKEINU appear 85 times in Tanach, including 5 times at the beginning of a pasuk, which is what is needed here. The choice of this specific pasuk might be motivated by its being the shortest of the five candidate p'sukim.

Without recourse to finishing a pasuk and thus saving the utterances of G-d's names from being in vain (because more than the first three or four words were said), the common practice is to say:
BARUCH SHEM K'VOD MALCHUTO L'OLAM VA'ED:
this does not mean that the Names were not in vain, but it at least acknowledges the sanctity of the Name(s) by stating that His Names are blessed for ever and ever.

These details should show us how concerned we should be about proper respect and reverence for G-d (and His names), and how we should be careful to avoid the disrespect of taking His name in vain.

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