I haven't played this game in a long while and I just noticed all my pets have "legacy names" and was wondering what that meant exactly? Is there something special about these names? More valuable/desired?

Some (usually RW or RN) are valued because legacy names are not attainable.

Legacy names were assigned to pets created before the non-unique names were implemented last July. Whatever the pet's name at the time of that implementation became their legacy name. Some people like it as a badge of pride for having the name at that time.

This topic may help you more: FAQ about Legacy Names/Non-Unique Pet Names

You can read up about legacy names here FAQ about Legacy Names/Non-Unique Pet Names. :)

Thank you both for responding to this and for giving me the links. It is much appreciated!