Is it permissible for a girl to call her mother by something other than "Mama" or "Umm" (Mother), such as a pet name or by likening her to lovely things?

Children are required to revere their parents in word and deed, for Allah Almighty says: "And your Lord has decreed that you worship none but Him. And to parents, show good treatment. If one of them or both of them reach old age [while with you], say not to them [even] 'uff,' and do not repel them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they brought me up [when I was] small.'"

Thus, every word that contradicts noble speech and the required respect must be avoided. Anything else is permissible, as long as it does not convey a lack of reverence and respect.