This isn't actually the name "Link". There's only one pet named Link...what you have is a retired name, more commonly known as a glitch name, and you can see this if you view the ti
tle bar of the petpage. Yours is named "li<x>nk".
Still can't tag it to anything else or change the casing, but yes, you can morph it. IMO, "glitch" names are worth a considerable amount, especially to collectors. Don't sell for a low price! =)