Mother's the word

Zak calls me 'Mummy'. Now that's what I can't reconcile with my being a mother to him. When he started calling me 'mummy' instead of 'Nanay' or 'Mama', the image that came to my mind was that Tutankhamen Egyptian. K calls his mother 'Mam'. He can't cope with 'Mommy', and Zak calls his Welsh grandmother 'Nana'. It appeared that the best option is 'mummy' because it goes with 'daddy'. But still, why spell and pronounce this word this way? I don't know how Zak would sound like with 'Mammy'. Is it Irish-y?