Is It Haram to Shower Naked?
Question

Can a person take a bath without any clothes on his body?
Praise be to Allah.Is it permissible to shower naked?
Yes, it is permissible for a person to take a bath/shower naked , because this was reported from the Prophet (peace and blessings of Allah be upon him). Maymunah (may Allah be pleased with her) reported that she and the Prophet (peace and blessings of Allah be upon him) took a bath together, washing from a large bowl in which there were traces of dough. 
And it was reported in several places as narrated by al-Bukhari and Muslim, and he bathed with ‘Aishah (may Allah be pleased with her).
Should we wear clothes while bathing?
There is no authentic hadith from the Prophet (peace and blessings of Allah be upon him) to indicate that it is obligatory to cover oneself when bathing. It was reported that some of the Salaf used to cover themselves, but this is not obligatory according to Islam. It is sufficient to be far from where people can see you.
Some scholars use as evidence the hadith in al-Sahihayn which speaks of Musa (peace be upon him) bathing naked (al-Bukhari, 274; Muslim, 339). Al-Nawawi entitled the chapter in Sahih Muslim in which this hadith occurs the permissiblity of bathing naked when one is alone.
It was also reported that Ayyub (peace be upon him) bathed naked. (Sahih al-Bukhari, 275)
Imam al-Nawawi said:
“We have already seen in the previous chapter that it is permissible to uncover the ‘awrah when necessary, when one is alone, such as when taking a bath, urinating , engaging in intimate relations with one's wife , and so on. In all of these cases, it is permissible to uncover one's ‘awrah when one is alone, but in front of other people it is forbidden to uncover the ‘awrah in all cases.”
The scholars said:
“Covering oneself with a wrapper or something similar when taking a bath alone is preferable than uncovering oneself. Uncovering oneself is permissible for the period of time that is essential to take a bath, etc., but uncovering oneself for longer than that is haram according to the most correct opinion.”
And Allah knows best.