What are the connotations of the word 拳拳? I chose 拳拳 as my own Chinese name, having the meaning of my name in mind. I got it from an online dictionary, so I would like to know what native speakers "get" from it, as in what are the connotations that a native speaker gets by such a name, since the dictionary cannot tell me that.

Some info might be useful: My name is Ernesto from old english Earnest which means honest, sincere, among other things.  

So I translated Earnest in various online dictionaries, and from the resulting meanings I chose 拳拳 mainly because I liked it from an aesthetic standpoint and also because the character 拳 is part of the name Tae Kwon Do in Korean (跆拳道), a discipline I practice.  

Is it reasonable to think that the word 拳拳 is related to the concept of "honesty, sincerity"?
When I first saw it, I thought it meant fist fist. By the way, I think the same word appearing twice in name usually is only appropriate in girls' names; it makes the name cute. If you are a guy, you probably don't want that.

But there is a 成语（4 word idiom with well known meanings) that says 拳拳之心 (heart of 拳拳) which is an adjective that means forever remembering in heart.