What is his English name? Perhaps we can work from that angle or get some idea. 慧 means wisdome but also implies compassion or benevaloence as from a mother (from Buddhist meaning) and so it is used for female names.  My four sisters has this character followed by 蓮, 霞, 義 (because 羲 meaning morning does not sound good) and 薇.  Not only the meaning is important but also the sounds because it can be construed as something else.  For example, in the Monkey King story, the 2nd disciple is called 悟能 (the ability to understand) comes across as the sound of 無能 (no ability) and this is bad.  My Tawainese friend has a beautiful name in meaning.  His last name is 江 (river) and his name is 河 (river) 清 (clear, pure) to mean "may all the rivers be as pure always".  However, it is considered extremely unlucky in Cantonese because 清 can also means "to be cleared, empty, all gone".  Water is considered by the Cantonese as money (as in wealth).  So the name can be mean as "no matter how much money you may have, it will be all gone"!

Hence choosing a name is very difficult and even with great care, children can always find something unpleasant about it.  My Chinese name means "bright and illustrous" but with a slight change of tone, it means "piss pot".  So I have to live all my life with his common moniker from my friends.

我想给我儿子一个有特制的名字

我想给我儿子（取）一个有特制（特质/特色）的名字 (Typo?)

他的英文名字比较有特色（「特色」is a noun ），不但是很吃香而且是一个独特的名字。（「不但……而且……」）

(second part of the sentence rewrite: 不但很吃香，而且很独特 )

我花了很多（「长」is more common ）时间去考虑一个又有优良的属性、又独特的中文名字，但是到时候（?）还没确定。

（「考虑一个名字」doesn't make sense, 「想一个名字」is better. ）

（「到时候」means "by the time" and it suggests the future, I think you mean 「现在/目前」.）

反正，我如果想好（了）这种名字，他也会被取笑活着（或者）让人感觉到异样，

(「反正」gives me a feeling that "whatever I do ,it makes no difference." It sounds negative. I'm not sure if it is appropriate in this sentence or not. Sometimes the word "anyway" in English is just an interjection )

(and 「如果....也...」seems wrong here)

特别因为他是白人，他要是在中国就已经是个外国人了。(I don't know how to correct this sentence.., maybe you can write it in English)

我也怕别人会觉得我和他太骄傲。我当然为他很骄傲，我已经在和朋友之间喜欢将他而吹牛（I don't understand this sentence.）...

给他(取)一个很独特的名字不是（「会」is more common）太过分吧？

我(在)考虑如以下的几个名字：（I‘m not sure, maybe 「考虑」means yout havn't decided yet ,so 「在考虑几个名字」feels right,  but 「考虑一个名字」like the above one makes no sense. ）

阔颖
伟耀
伟熙
胜詹
我本来想用“慧”的一个字但是有人说“慧”只可以在女人名字才用。我就想，“慧”知识智慧的慧，怎么表达女性味？？？(...well i don't know either )其实，对我来说中文名字很难了解，很难记住。

(「阔」=rich (negative), DON'T USE IT! ）

(「颖」feels girlish, too.)

我想给我儿子一个特别有特制的名字

我想给我儿子一个有特制特别的名字