IT IS MUSTAḤABB to say ‘In the name of Allah’ [when putting on clothes]. Likewise, it is mustaḥabb to mention the name of Allah in all actions.
We relate in the book of Ibn as-Sunnī that Abū Sa‘īd al-Khudrī 
, whose name was Sa‘d ibn Mālik ibn Sinān, reported that when the Messenger of Allah 
put on clothes he would name each item—whether it was a shirt, pair of trousers or turban—and say: “O Allah, I ask You for the good of it and the good of what it is meant for, and I ask Your protection from the evil of it and the evil of what it is meant for.” [1].
, whose name was Sa‘d ibn Mālik ibn Sinān, reported that when the Messenger of Allah put on clothes he would name each item—whether it was a shirt, pair of trousers or turban—and say: “O Allah, I ask You for the good of it and the good of what it is meant for, and I ask Your protection from the evil of it and the evil of what it is meant for.” [1].
Allāhumma innī as’aluka min khayrihi wa khayri mā huwa lah, wa a‘ūdhu bika min sharrihi wa sharri mā huwa lah.
And we relate from the book of Ibn as-Sunnī that Mu‘ādh ibn Anas reported that the Messenger of Allah said: “Whoever puts on a garment and says: ‘Praise be to Allah, Who has clothed me with this garment and granted it to me without any power or might on my part,’ Allah will forgive all his past sins.” [2].
reported that the Messenger of Allah said: “Whoever puts on a garment and says: ‘Praise be to Allah, Who has clothed me with this garment and granted it to me without any power or might on my part,’ Allah will forgive all his past sins.” [2].
Al-ḥamdu li-llāhi-lladhī kasānī hādhā-th-thawba wa razaqanīhi min ghayri ḥawlin minnī wa lā quwwah.
References
[1] Ibn as-Sunnī (14), Abū Dāwūd (4020), at-Tirmidhī (1767), and al-Ḥākim (1/192), who regards it as fulfilling the criteria of Imam Muslim; and adh-Dhahabī agrees.
[2] Ibn as-Sunnī (272). Ibn Ḥajar grades it as ḥasan.