This is a truly excellent poem about racial differences during a time of Britain's history when racial lines were clearly drawn between whites and other ethnic backgrounds, and respectability was based on how "white" you actually were. However, if we examine this poem as a dramatic monologue, there are several aspects that point towards the way that this poem does not fit this description. Let us remind ourselves of the definition of a dramatic monologue. A dramatic monologue is a poem in which a speaker who is not the poet addresses a listener who does not speak. Normally, dramatic monologues do not contain any authorial intervention. We are left to draw our own conclusions about the speaker from what they say and how they say it. An excellent example of a dramatic monologue is "My Last Duchess" by Robert Browning.
Considering this definition and applying it to "Telephone Conversation" shows that there are lots of ways in which we cannot consider this poem to be a dramatic monologue. Firstly, the main speaker is also the narrator of the poem. Secondly, he is not the only speaker, as we can hear some of the words of the woman he is calling. Thirdly, the speaker does not just leave us to draw our own conclusions about the scene, and intervenes to point us in the right direction. Consider the following example of this:
"Madam," I warned,
"I hate a wasted journey—I am African."
Silence. Silenced transmission of
Pressurized good-breeding. Voice, when it came,
Lipstick coated, long gold rolled
Cigarette-holder pipped. Caught I was foully.
We are not left to draw our own conclusions about the lady and her racial presumptions. The speaker even goes as far as to imagine the woman by the kind of voice she has. His comment "Caught I was foully" transmits the irony of the poem. Thus, for these three reasons, I don't think we can consider "Telephone Conversation" to be a dramatic monologue. It certainly has elements of this poetic form, but apart from these it is not a dramatic monolgue.