Rhyming Problem!

Our cousin gifted us a Cocker Spaniel female. Like all pups, she so endeared herself to all of us that for some time she was the only topic of discussion in the family. Manisng, my son promptly named her, Lizza. (For some strange reason, it is customary, to give English names to cats and dogs in our family, we have a German Shepard named 'Tyson', and a couple of mixed breeds named 'Jockey' and 'Lion' ).

Though we have always owned many different breeds of dogs, this is the first time we have got a Cocker Spaniel. Our parents, as part of proper grooming, had taught us to rinse our mouths after every meal, but now we realised for Cocker Spaniels, this was not enough!, their ears too need washing after every meal, as the poor animals just cannot help dipping them into the food while eating.

A few days later, we brought home Lizza's sibling, as both of them were lonely without each other. I named her "Daisy"- and there began a rhyming problem!. The two are always together, and they need to be addressed simultaneously. They were either called "Lazy-Daisy", or "Lizzy-Dizzy". Now with her tremendous verve and energy, Lizzy was certainly not lazy, and neither did Daisy show any signs of  dizziness.

Our staff, who, did not like the English names anyway, promptly changed them, to  "Champi-Dampi", to be immediately admonished by my  better half, Varsha. She felt it sacrilege to change a name so lovingly given by her son and hubby.
Any suggestions here?