Is it Sunnah for a woman to cover her head while cooking in her home when she is alone, even if there are no non-mahram men present?

There is no objection to a woman wearing whatever clothes she wishes in her home, as long as she is secure from the sight of non-mahram men. Hijab was legislated to conceal a woman from non-mahram men, as Allah Almighty says: (O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful) and His saying, glorified be He: (And not expose their adornment except to their husbands or their fathers or their husbands' fathers or their sons or their husbands' sons or their brothers or their brothers' sons or their sisters' sons or their women).

Therefore, there is no objection to a woman uncovering her head while cooking or doing other activities if she is alone at home and is secure from the sight of non-mahram men. What is obligatory upon her is to adhere to the complete legitimate hijab in the presence of non-mahram men, whether inside or outside the home.