Why 意大利 and not e.g., 意国
It's just historical stuff. European countries that have commerce with China prior to the Ching dynasty and also modern countries after WWII, in general have fancier names.

希腊 for Greece
意大利 for Italy
瑞典 for Sweden
法国 for France
美国 for US
葡萄牙 for Portugal
马来西亚 for Malaysia
日本 for Japan


etc.

You just have to accept them as it is. It's hard to find a pattern why. 

Edit: http://www.nationsonline.org/oneworld/countrynames_chinese.htm

There's very few countries which have 国 in their names, it's more of a short form, like 英格兰 for 英国, 美利堅合眾國 for 美国. Others which have 共和国 in their names are People's Republic, like China, whose official name is People's Republic of China.