hi,your pronounce is right.
xiǎo ,小，means small,some times it also used for a name"小红";
the word for name,i guess you said is "xiǎo"晓，is it right?it's not a special word for a name,just used more often. it means to know ,dawn.when it used for a name,usually it means dawn.
as the instrument,箫,xiāo .
'to serve one's parents well' this is 孝, xiào.
there are many homophone,remember them by heart,step by step,u will be great at chinese.