Before I started wearing a Kippa all the time, the people around me and I had the reflex to cover our head when saying the name of G-d or when reciting anything holy.
Since the mitzvah is to wear it at all times, then why would it matter more while reciting a blessing? Is there an additional ordinance to wear it while reciting Hashem?
If my Kippa fell and I recited a blessing without a kippa, would it matter more than if I walked around without one?
Orach Chaim 91:3 - The Beis Yosef says that Yesh Omrim that you are not allowed to say Hashem's name with your head uncovered.
The Mishna Berurah in siman 25 s"k 27 says that when putting on the Tefilah Shel Rosh, one should be careful that his head is covered before making the beracha. He gives the source as the Pri Megadim.
בס"ד Taken from here
Although one should be careful to make all berachos with a head-covering (kippah), if a berachah is recited without covering one’s head the berachah is valid, and is not repeated.
The same applies for all prayers.
Best wishes.
Sources: Even (some of) those authorities who write that there is no obligation to wear a kippah all the time, rule that one must do so when reciting a berachah (Kol Bo 11; Or Zarua 2:43; Tur, Orach Chaim 8; Rabbeinu Yerucham; Taz 8:3).
One must therefore be careful to cover one’s head when making a berachah (see also Orach Chaim 91:4, and Mishnah Berurah 91:10).
However, there is no question that a berachah recited without a head-covering remains valid, and cannot be repeated.
