The girl who sat next to me [is or was?] named Stephanie.
Many implicatures are driven by a principle of relevance, first formulated by the philosopher H. P. Grice. The principle is that if someone tells you something, you can assume that it has some relevance to the conversation. If the statement itself doesn’t seem to be relevant, then you look for additional intended meanings that might make it relevant.
Here’s how the principle of relevance applies to implicatures and the past tense, as stated by linguist Bernard Comrie in his book titled simply Tense:
[T]he past tense only locates the situation in the past, without saying anything about whether that situation continues to the present or into the future, although there is often a conversational implicature that it does not…. This last part follows from Grice’s maxim of [relevanc, in that, other things being equal, statements about the present are more relevant than those about the other times, so that the use of a form explicitly locating a situation in the past suggests that the situation does not hold at the present.”(1)
Many times, implicatures do useful work for you. For example, when I was reading a novel and the narrator said about a woman, “I loved her,” I took his message that the character was doomed, and read more, wanting to know how and why she died. The author used the principle of relevance skillfully. In the radio commercial, the grandfather violated this principle by using a past tense form when he knew full well that he could use the present tense. Confusion ensued.
Another important thing about implicatures is that they can be canceled without contradicting what has been said. For example, if your friend who’s coming in to town is actually kind of a jerk, he might add, “But I don’t want to get together with you.” Regarding how red ants taste, Aardvark might continue, “At least, that’s what I hear. I’ve never eaten red ants.” And the grandfather playfully canceled his milkshake implicature when he said, “Yep! They still do.”
So let’s get back to Becky’s example. She is clearly worried about accidentally implicating that Stephanie is dead or maybe named something else now. So would her audience infer such a thing?
If I were reading or listening to a story, told in the past tense, and came to the sentence “The girl who was next to me was named Stephanie,” my first assumption would probably be that Becky used the past tense simply because the rest of the story was in the past tense, and there was no compelling reason to switch.
But different contexts and even different word choices give different implicatures. If she had written, “The girl who was next to me used to be named Stephanie,” I would assume that Stephanie had changed her name since then. Furthermore, if Becky wrote, “The girl who was next to me is named Stephanie,” she would run the risk that the reader will use the principle of relevance on the choice of present tense. For example, I might think, “Hmmm, Becky has switched from past tense to present. She could have just used the past tense and let me assume that the girl is still named Stephanie, but instead, she switched to present tense. Maybe that means that Stephanie had a different name at the time this story happened.”