IMDb and Wikipedia explain the De Morgan laws as follows:
The names Dexter Morgan and Debra Morgan refer to the two laws of De Morgan – valid rules of inference in propositional logic. Informally, the laws are “not (A and B) is the same as (not A) or (not B)” and “not (A or B) is the same as (not A) and (not B)”. They describe their mentality towards the existence of each other: Neither Debra nor Dexter can live without the other. Both characters express that several times throughout the series.