I am pretty sure this is a chaste tree. You can find pruning advice here: https://www.thespruce.com/chaste-tree-growing-profile-3269206#toc-pruning

In short, cut spent flowers now if you want more whenever the go brown. In winter, cut as much off as you want, even back to the ground. If it causing problems (like hitting the window) now you can cut those parts immediately, but I would wait until winter to do a hard cut.