Always right from the left...!!!! LOL...!!!!

I can not even write with my left hand. I have tried before no luck.

I am ambidextrous but never really used my left hand for so long to write. For my left I use for cutting and crocheting and for carrying heavier things. but writing it's my right

You could see yourself that you could write your name neatly with your right hand, as you are a right handed person. When writing with your left hand, there were some jerky movements and your letters have less uniformity and your letters have gone below the base line, while writing. It proves that left side of your brain is more functional, which guides you to write with your right hand. I have some interest in graphology (study of handwriting) and according to graphology if one is writing in capital letters, s/he does not want to reveal his/her real emotions or real-self. However, you might have written your name in capital letters, because you just want to have a clear picture of your hand writing and it is a matter of chance only, so my analysis about writing in capital letter may not hold true here.

you did well writing with your left hand... I don't think I can do that well writing with my non-dominant hand...

I don't write very well with either hand. However I learnt piano for many years so when I began to learn to type my little fingers were quite strong. Many of the other people in the class had trouble making their little fingers push down the keys - this was on manual typewriters.