How to change sorting options display name?

To change sorting options display name as well as any other extension texts when using the Improved Sorting please open the file app\locale\en_US\Amasty_Sorting.csv

Add, for example line,

"New", "New In"

and refresh the cache.

To change the default wording (price, brand) you may use

1) app\locale\en_US\Mage_Catalog.csv will change all occurrences, not sure it's applicable in that case

2) open admin > catalog > attributes > manage attributes > and set appropriate store labels

3) use inline translation tool (not recommended, as it will be hard to find the translation when you need to change it)