Corporation name: Just notified by legal zoom that another corporation has a similar name and I said to apply anyway

I'm incorporating a holding company. Legal zoom told me my name "The XXX Corporation" is very similar to "XXX, LLC" (not actually the names). The guy on the phone asked me if I wanted to send the application anyway and I said yes. If it's accepted, should I do anything to protect myself? "The XXX Corporation" won't really be selling anything and won't have a big presence online--it's just a holding company to centralize all of my projects. I'm wondering if I should register "The XXX Corporation" as a trademark just to cover myself.

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