I love double meanings. In titles, in character names, in dialogue. If done correctly, intended double meanings can have a one-two-punch effect, making already-deep text plunge even deeper, reaching the reader on an entirely different level.
Here's an example: I happen to love that old 80's t.v. show, Thirtysomething. Well, in Season 3, a character named Ellyn finds herself in murky water, dating a married man. For many episodes, she deals with the moral issue itself, with judgment from her friends, and with the empty promises of the married man (to eventually leave his wife for her).
In a particular episode, he actually does the unthinkable and leaves his wife to be with Ellyn. Unexpectedly, both he and his 12-year-old daughter move in with Ellyn, while they all try to sort out the chaotic details of this sudden decision. Well, Ellyn visits her therapist when the romantic bubble starts to burst - when she realizes that the decisions she and the married man have made start to affect other people. Like the daughter.
Which brings me to this -- there's a powerful scene where Ellyn is talking to her therapist about the daughter, venting about how aggravating she's been. Ellyn spouts off something like: "This girl is sweet, but annoying. She's bugging me! And she's careless. She loses things all the time! Her school notebook, even my very-expensive bracelet. She left it in the cab yesterday and now it's gone. Can you believe that? This girl loses everything!" *a pause as Ellyn realizes what she's just said* Then, she whispers, slowly: "She loses everything..."
The first time she said it, the statement meant one thing. It was about jewelry. But the second time she said it, the statement meant an entirely different, more poignant thing. The daughter was the one paying the price for Ellyn's decision to date a married man. The daughter was the one "losing everything." Double meaning. I love it. And then, of course, those physical objects of the notebook and bracelet have now become actual symbols of a greater loss woven throughout the episode. Thirtysomething is filled with that kind of deeper meaning in nearly every episode.
I think it's an excellent lesson for writers - not that we have to try too hard to inject double meanings into absolutely every line. In fact, if the symbolism/double meanings are all over the place, or are overly-obvious, they become less effective. But sometimes, when the scene or dialogue or description allows, a double meaning can be pitch-perfect and create a deeper throughline to the rest of the story. Powerful stuff.