The great thing about most food recipes is they're easy to name. A simple description of its constituent parts: arctic char rice bowl, mozzarella pluot salad, bacon cinnamon rolls. But drinks, drinks are a different story. The name "honeydew cucumber gin cocktail" just doesn't roll off the tongue. It doesn't sound as graceful as an Old Fashioned, or Aviation, or Manhattan. I think for drinks, a name is almost as important as the way it tastes.
I don't really believe in throwing out a series of random words until something sticks. Memories are a much stronger place to pull names from. Even if it evokes no particular feelings for anyone else besides myself and and a few others. For us, it's important enough.
Eons ago, when we were studying abroad in London, we stayed in these cookie cutter private dorms by Kings Cross. The closest bar was a place called The Long Hope, right across the intersection. It was an average bar, nothing about it particularly stood out, but it was a place that forever engrained itself into our memories, a symbol of the summer we spent abroad in a city that made a profound impact on the rest of our lives. So this drink is named after that bar, a summery drink to commemorate a bygone summer from years ago.