I know you have them. Fess up.
This is the favorite one I have in my collection: the variegated flower 'Shibori'.

Can someone tell me why the flower is turning brown? Should I cut it off at the bottom of the stem?

That is not the 'flower', the colorful part is the spathe, a modified leaf bracht that draws pollinators to the true flowers, which are tiny the size of a pinhead and occur in rows on the spadix (that projection that resembles a stick). Once the true flowers do not get pollinated, the entire spathe and spadix complex begins to denigrate and die back, so you you can snip it off