Adopting an appropriate Chinese name I'm starting to learn Mandarin and I'd like to adopt a Chinese name. I wonder if 滿熊汗 (Mǎn Xiónghán) would be an appropriate one.

I've read that 滿 is a surname with Manchu ethnic origin, and I know that 熊 is a common surname and I don't know if it would be possible to use it as a part of the given name. Other than that, I don't know if this name sounds weird, strange, childish, eccentric or whatever to a native Chinese speaker.

谢谢!
Good to know you starting learning Mandarin!

However, I do not think the name is good... Actually a lot of foreigner get their name weird.

A common structure of a Chinese name is Family name + Given name.

So, I think "满" is a good one for a family name because it is a existing family name (满文军, for example, a famous singer). Also, it kind of part of your own family name, according to your profile.

Although 熊 is a surname in Chinese, but it means bear the animal more often. It is okay to put animal in name in China, but often 虎 for guys and 燕 for girls. 熊 is definitely out of the range. Also, 熊 as a adjective, means crude, impetuous and naive.  So, don't use it. If you want the pronunciation, I would recommend use "雄" instead of "熊".  "雄" means hero or brave or strong. It is used by 扬雄, an ancient writer.

You do not need put all parts of your family name in your Chinese name. 
Basically, it is not possible, considering common Chinese family names are less than 2 characters, most of them are just one character. I think if you think OK, 满 is very good.

汗 is not good, neither. It often means sweat. Although the pronunciation you want to use means king or leader.  The Good character is "汉", which is used by 田汉, the author of the lyric of national anthem of China.

However, it still kind of weird...