When making a bracha with shem u'malchut, one should not have erva (nakedness) exposed. For married women, their hair is considered to be erva. So does a woman who is married have to cover her hair when she makes a bracha?
Many ladies when they go to the Mikva have their hair uncovered when they make a Bracha.
See also Mishna Mesechtas Chala האשה יושבת וקוצה חלתה ערומה - from the Biur it clearly seems like she takes Challa and makes a Bracha in that state.
However Yabia Omer 6:15 says that a lady should have her hair covered even if in Chadrei Chadarim when saying Hashem's name.
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Ovadia Yosef holds that women, married and unmarried, ideally cover their heads when they say shem u'malchut, regardless of location or others' presence. In a Yeminite shul, unmarried women will be asked to cover their heads and I have seen unmarried Yeminite women cover their heads to light and bless Chanukah candles.
For those who are interested in the issue of whether women's headcoverings have significance outside of modesty, this looks like a good article, though I personally haven't gotten to it:
Hair Covering for Single Women: A New Reading of Mizrachi Halakhic Rulings. Ilan Fuchs. Nashim: A Journal of Jewish Women's Studies & Gender Issues. Number 23, Spring-Fall 5772-3/2012