Your initials begin with an A,
You've an A at the end of your name,
The whole of your name is an A,
And it's backwards and forwards the same.

Anna.

Ever running on my race,
Never staying at one place,
Through the world I make my tour,
Everywhere at the same hour.
If you please to spell my name,
Reversed or forward it's the same.

Noon.

You name me once, and I am famed
For deeds of noble daring;
You name me twice, and I am found
In savage customs sharing.

Tar-tar.

What is that which lives in winter, dies in summer, and grows with its root upwards? An icicle.

Water soft is my first, water hard is my second,
Sticks made of my whole are by many sweet reckon'd.

Liquor-ice (licorice).

From a number that's odd cut off the head,
It then will even be.
Its tail, I pray, next take away,
Your mother then you'll see.