With two first names, a double-barreled surname, and far too many nicknames, not to mention a pretty fast talking speed, Cassie has to be careful whenever she introduces herself, or people will end up thinking she's called Cassie McGregor, or even 'Cassandra Mart'. (It's happened before.)
She prefers people to call her plain Cassie rather than Cassie Heather, since, as she puts it, it 'takes too long to say'. However, she's also proudly adopted the nicknames Cass, Cassieopia, and Cabbage, among others.
'Cassie' itself means 'prophetess'. Although Cassie's parents firmly believe that nobody can see into the future (having never encountered a Seer before, they remain convinced that anyone who claims to be one is lying), they did want her to be prepared for any eventuality. She hasn't quite managed this yet, but she's about three-quarters of the way there. (A 'cassie' is also, apparently, a type of straw basket. The McGregor-Martins didn't know this when choosing Cassie's name.)
The part of her name with the most meaning is her second forname, Heather. This name was chosen by her mother, Harriet McGregor, who likes to remind her of just how resilient, how strong heather plants are. How they're beautiful, but they're also hardy, and they're pretty prickly if you poke them. Not that she wanted her daughter to be poked, of course - she just wanted her to be strong if she was. (This is usually the point in the speech where she decides she's gone too far with the metaphor and moves on.)
Cassie's surname is double-barreled. When she married Pierre Martin, Cassie's mother didn't want to lose her surname. Instead, the pair stayed as Mr Pierre Martin and Ms Harriet McGregor, were referred to as the McGregor-Martins, and passed on both names to their daughter.