how to write my name

my name is alexa and I'm wondering how my name could be pronounced and written in romaji by a japanese person? also, I'm a young (early 20's) female so should i refer to myself as -chan or -san in general situations?sorry if this is a stupid question

The name would be A Re Ku Sa
My name is Alex and is A re ku su

and dont call yourself like
watashi wa X san or chan.
since its like honoring yourself, talking about yourself only use your name withouth san, chan.

Usually to form x the k is doubled in Japanese, so Arekkusa in romaji, アレックサ　in katakana.

As above, san and chan are strictly for addressing other people. You should never use either to refer to yourself. If you call yourself "Alexa san" it just sounds odd, if you call yourself "Alexa chan" you sound like a 2-year-old!

yes i thought this would be the case and then saw a wonam on TV refer to herself as Julia-chan - completely confused me!! thanks again for your help