should have a plasma and urine osmolality checked, BMP and urine electrolytes all done concomitantly. A comparison of plasma to urine osmolality will give invaluable information.
Urine osmolality greater than serum osmolality, especially if ure osmolality is greater than 400, would be suggestive of an SIADH, which would be treated with fluid restriction of about 1000 ml/day.
A urine osmolaltiy less than plasma osmolality would be suggestive of low osmolar load having led to hyponatremia as is seen in beer potomania and the "tea and toast" diet, which would be treated by having the patient eat more actual food rather than getting empty calories from something like beer.