Arman 1

Both comments are close but not so accurate. It is true that the name is widely used everywhere. However, the root Ar is Armenian which is also used in Farsi language. Armenians and Persians (modern day Iran), living next to each other for millennia, have over 2000 common words. However, Ar is borrowed from Armenian language, meaning sun. Such as Arev (Sun) Aravot (morning (sun is up)). Armenians used to worship sun (pagans) before accepting Christianity. Foreigners were calling them Arman or Armen as "people of the sun" This is why foreigners named the country Armenia while Armenians call themselves after their ancestor hayq. Same as like Japan or Netherlands.
Arman means god's man or man that is born from the sun.

The word Arman and Armani are Persian. [noted -ed]

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Although your information suggests that it is Kazakh, that would be incorrect. However since the Persian empire covered areas such as Tajikistan, Uzbekistan who speak Persian dialects, then it's just as likely that the Kazakh were also influenced by the language of the empire.

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Arman means hope or wishful thinking and desire through hope. Armani is a person that hopes or has wishful thoughts and desires through hope. It can also mean to dream as your site suggests but hope is more accurate.

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Arman can also refer to a vision. And thus Armani is a visionary (perhaps useful for the famous name of Giorgio Armani and why he may have chosen it).

The name is a Persian name actually. First originated in Northern Iran. Kazakhstan later got the name through culture exchanges with the two countries, and both countries are alike.