The character's opening remark, "Deep background," suggests that he is involved in a situation of keeping secrets about the details of people's lives: where they live, their identification numbers, family members, financial history, etc.. In this context, "come close to" is an idiom that means Billy will be very cautious not to use the other person's name or take any other action that will risk endangering him (or her) by revealing a hidden identity. Depending on the story you're reading, Billy might be protecting himself by not revealing a source of information or another person.Originally Posted by english-learner
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