Is it normal for Arabic-speaking grandmothers to prefer being called Ummi?

[Thuraya17]

This is basically aimed towards native Arabic speakers, where Arabic is your first language and culture. Is it normal for a grandmother to request her grandchildren call her Ummi (my mum)?

Yes. Ummi is more formal. Mama is normally what we say to our mums. Mama, mami..
my grandmother from my dad’s side, we used to call her “mmi “ which is short for of ummi- and my grandmother from my mums side we used to call her mima which is also again similar meaning to mama. In almost of Arabic families the grandmother is treated like a second mother, calling her Ummi expresses closeness, affection and respect.