Generally I've only done /renameme when I purchase a ship from another player or for initial naming (due to tag password). Usually I have a ship name / class in mind already when I use a slot.
I usually come up with the name first, then pick the ship I think fits, but I rename for two reasons:
Ship transfer, whether from myself or someone else, my pilots/accounts have a vague theming for their ships.
I also rename for faction tags, but that's such a common use case across the board that I don't think that's intrinsic to how/why I use it.
One of these days, there will be a clever, stylish and/or funny signature here.
This is still not that day, however.
not only when i buy a ship from another player, but also to use a name that i like from a ship that is useless or i sold, to another ship that already had. but not often i do that!
I only do it when I am making a new character or repossessing an old ship to a different character, which is kind of rare. Other than that I stick to whatever name I picked at first