Modifying WordPress Links (not permalinks)

Hi all,

I’m working on a website for a local animal shelter that I have built using WordPress.

http://www.bluecrossanimals.com.au

I would like to adjust the “read more” link that takes you to the post page so that it says “Read more about (dog/cats name)”. I presume I would somehow have to call the post name into the link, but I am unsure how to achieve this. Anyone got any tips?

Cheers,

Chris