In MN 82 [SC 19.3] the text reads:
“atthi nāma, tāta raṭṭhapāla, ābhidosikaṃ kummāsaṃ paribhuñjissasi?
Ven. Sujato’s translation contains an ellipsis:
“Dear Raṭṭhapāla! There’s … and you’ll be eating last night’s porridge!
[NB: the same formula occurs in the story of Sudinna contained in the first training rule [ SC 5.6.13]]
My question is: what is the obstacle to understanding atthi nāma along the lines of ‘is it really so?’
The father would be expressing their surprise that their son is eating yesterday’s leftover gruel.
FWIW, Buddhaghosa seemingly glossed atthi nāma as atthi nu kho.