someone's mum whose name is Mum?

[sunshineoutdoors]

Is this correct? Do I only use a capital M if using the word as a name? e.g. "Mum!" Do I write about somebody's mum or somebody's Mum?

Mum if you're addressing your own, mum if it's someone elses.

No! OP is right, you only capitalise if you're using the word as a name. So:

"You need to tell Mum her lunch is ready."
"Do you want a cup of tea, Mum?"
"I need to ask my mum if I can go."
"Will your mum be coming too?"

it's "somebody's mum" because you're using the word as a general noun, not a Proper noun.

Exactly how Euph says.

"Mum!" would have a capital anyway, because it's a complete sentence.
"Get Mum!" has a capital, because you're asking someone to fetch a person whose name you are using.
if you said "Get my mum!" there's no capital, because you're using a term for a person, not using it as a name.