Aliza is actually a legitimate name, completely separate from Eliza. It is Hebrew, means 'joyful' and is pronounced ah-LEE-zah.
My husband and I are culturally Jewish and are actually considering Aliza for our second child.
If you're going to use Aliza, and pronounce it properly (as above), then go for it safe in the knowledge it is a real name.
However, if you're just trying to get creative with Eliza, then don't bother. Regardless of how you spell it, if you used Aliza with the intention of pronouncing it as Eliza, then your daughter would still be called Eliza. She would still have a popular (I prefer that term to 'common') name, just with an awkward spelling.
Spelling a popular name differently never makes sense to me, because when the name is spoken, they're still just another aren't they?