Whilst alone, is it wājib to keep at least the area from below the navel to the bottom of the knee covered, unless one is taking a bath or relieving him/herself, or other situations where a legitimate need arises, due to the ḥadīth narrated by Ibn ‘Abbās رضي الله عنه that the Prophet ﷺ said:
“Indeed Allāh forbids you from nudity, so show modesty from the Angels of Allāh that are with you and never leave you – The Kirām-Al-Kātiībūn, except in one of three states: relieving yourselves, janābah and whilst performing ghusl. When one of you takes a bath in the open, he should adopt privacy with a sheet, or a wall or his conveyance.” (Al-Bazzār)[1]
We learn from this ḥadīth that the obligation of covering oneself is general in all situations, even in privacy, except for a valid reason, which is at the time of relieving oneself, ghusl and other similar situations. This is out of modesty and shame from the angels that are with us at all times, as mentioned in the ḥadīth.
This rule applies to both men and women. Therefore, to walk around naked, even whilst alone, is impermissible.
(I‘lā’us-Sunan, Vol. 1, Pg. 244-7)
[1] Imām Al-Haythamī in Majma‘ Az-Zawā’id has classed this ḥadīth as ṣaḥīḥ (authentic):
قُلْتُ: جَعْفَرُ بْنُ سُلَيْمَانَ مِنْ رِجَالِ الصَّحِيحِ، وَكَذَلِكَ بَقِيَّةُ رِجَالِهِ. وَاللَّهُ أَعْلَمُ.
Knowledge Through the Pen 