All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The name “Aws” is an Arabic name that a group of the Companions bore. Therefore, there is no harm in bearing the name "Aws".
As for the name “As-Soosi,” it is the name of Imaam As-Soosi the Quran reciter who narrated the mode of recitation on the authority ofAbu ‘Amr Al-Basri . As-Soosi was given that nickname in reference to his hometown Soos in Al-Ahwaaz region (Iran).
Qaamoos Al-Ma‘aani (an Arabic lexicon) defines the word Soosi as follows: “A female Armenian name; it refers to a tree that grows in Armenia.”
It is also known that Soosah is a city in Tunisia and the one attributed to it is called “Soosi”. So there is no harm in bearing the name “As-Soosi”.
The basic principle is that there is no harm in keeping any name that does not denote a prohibited meaning or constitutes a Shariah violation. It is preferable to choose a nice name and avoid what may be disagreeable of names.
Allah knows best.