You can use
CTRL-F from that input box to open the command-line window, which lets you use Normal mode commands and even access history to reuse a name you previously typed.
I suggest you read
:help c_CTRL-F to see more details on how it works. Note that most of that help section talks about it in the context of the command-line (where you can type Ex commands), but most of that is also available for
input(), which is what NERDTree uses to prompt for your input.
Some parts of it are not relevant in this context. For example, the
q: command to open the command-line window from Normal mode. You can only access it with
CTRL-F from the
input() prompt. Otherwise, most of the information in that section (about navigating and closing the command-line window) is relevant.