A default judgement requires that a case be filed. In the US, that means they have to serve you notice of the case.

Obviously they have the OP's address, so if they fail to serve him the judgement should be easy enough to set aside.

I'd do absolutely nothing in this circumstance until and unless they actually initiate a legal proceeding. If they did sue for the domain, depending on the value of brand I probably lawyer up, and perhaps seriously consider counter-suing them for both their domain and the use of the business name itself.

"Strictly speaking, a cease and desist letter is not legally binding because the recipient can choose to ignore it. However, it is a valid legal document that establishes a precedent of a plaintiff's grievance. Usually, the letter sets a time limit for the recipient to comply with the request to desist from the offending action — or deliver an appropriate response if they believe the letter was sent in error."

Take the letter. Delete it. Engaging is the fastest way to lose the domain. Their Lawyers want you to engage and start making written statements. Don't.

"Seems like an excellent way to lose your domain in a default judgement"

Lol. Don't ignore legal paperwork or court dates, which this isn't.