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.

Not in my Arab country. It is Henna.

Not in our country. Unless you grew up in the extended household or no biologicql parents alive.
Also we use Lala for elder women especially grandmothers as q term of endearment

Ummi means my mother so no.

I’m not an Arabic speaker but my mother, although born in England, was from an Arabic culture. My Dd called her Ummi

It's totally normal for older women grandparents to call themselves anything that denotes mother. Ummi/Yamma/Mama etc.

In Lebanon people call their grandmother tetah or sitto. Ummi means “my mother”.
eta My kids call my mother “Mamma”, so it is not unheard of.