Andrew notes that marrying the future mother of his child would have put Mynor Montufar on the path to citizenship. The various considerations that go into figuring out why that was a road not taken highlight the fact that, while not all decisions follow rational thought processes, incentive structures still apply broadly.
As Andrew describes in the comments to his post, the process of becoming a citizen based on a spouse’s status does require a number of forms and a $1,000+ in fees. An illegal immigrant would also not likely wish to enter into the system (although this one was willing to have his mug published in the state’s major newspaper). Getting caught isn’t the only disincentive, however. Although I don’t know whether it applies in this case, adding a father’s (or a husband’s) income to the household total might decrease government benefits, and in Rhode Island, children (i.e., their parents) continue receiving support even when it has expired for the adults.
Illegal immigration and poverty advocates look at this set of incentives and see harmfulness in the restrictions. The fees and forms (and risk of getting caught) provide disincentive to get married, as do the decreases in public support. To them, illegal immigrants ought to be able to live openly, applying for licenses and benefits as if they were citizens, and recipients of government money ought to be able to collect up to higher boundaries. To the contrary, such an approach only makes the incentive structure more perverse: Immigrants have no reason to pursue citizenship, and many to avoid it, and women have incentive to produce even more children whom they lack the resources to support.
The villain in the scenario is ultimately the act of immigrating illegally. Its co-conspirator is destigmatization of living on the public dole. A third culprit, easily forgotten after its victory, is destigmatization of out-of-wedlock procreation.
Again, I’ve no information about the government support of the specific family in question, but it oughtn’t be a matter of contention to suggest that the subculture affects their decisions regardless. In that context, the names of young Marisol’s closest relatives convey discouraging information:

• Father: Mynor Montufar
• Mother: Carmen Marrero
• Maternal grandmother: Lilliam Muniz

A shared name does not a family make, of course, but I don’t think it’s mere knee-jerk traditionalism to suggest that it is not entirely devoid of importance and that it often comes in conjunction with other qualities for which society ought to provide incentive, sometimes in the form of disincentive for alternatives.