Adam Clarke on Luke 1:19

I am Gabriel - This angel is mentioned, Dan 8:16; Dan 9:21. The original גבריאל is exceedingly expressive: it is compounded of גבורה geburah, and אל el, the might of the strong God. An angel with such a name was exceedingly proper for the occasion; as it pointed out that all-prevalent power by which the strong God could accomplish every purpose, and subdue all things to himself.

That stand in the presence of God - This is in allusion to the case of the prime minister of an eastern monarch, who alone has access to his master at all times; and is therefore said, in the eastern phrase, to see the presence, or to be in the presence. From the allusion we may conceive the angel Gabriel to be in a state of high favor and trust before God.