We hear the phrase "acquainted with the night" three times in this poem – and it's in the three most important places: the title, the first line, and the last line. OK, Frost, we get it – the phrase "acquainted with the night" is important!
But the title is only a part of the first and last lines, leaving out the "I have been one." So, in a way, each time we hear the phrase "acquainted with the night," we hear it differently. In the title, we don't know the context. In the first line, we get a little more context, even if it's only the information that "I have been one." Then, by the last line, we get a different and more complete meaning of what it means to be acquainted with the night, and can imagine the entire scene of the poem – the rain, the city, the moon – when we glance back at the title. Now, instead of thinking that the title is just a cool sounding phrase, we know what it means, and can connect it to both the meaning of the poem and our own acquaintances with the night.