How do I pronounce names that end with "t" in the standard American dialect?

As you may already know, a stop consonant like [t] consists of three parts: the approach, where you bring two parts of your vocal tract together to cut off the airflow; the closure, where the airflow is stopped; and the release, where you let it out again. For voiceless stops (again like [t]), the closure is completely silent, so the only parts we hear are the approach and the release.

When a stop comes at the end of a word in English, and doesn't have anything after it, it's generally unreleased: there's no audible release, just the approach and closure. And if the stop is voiceless, the closure is silent, so all you hear is the approach.

If this is what you mean by "half-stop t", then yes, you're correct: the end of "Robert" is an unreleased [t̚]. But it's generally not a glottal stop (the sound in the middle of "flatten" in many dialects) or a flap (the sound in the middle of "ladder" in much of America), which have been suggested as other possible meanings of "half-stop t" in the comments.