With “splittig apart” you probably mean the visible seam at the top left corner. You can use the texture node “generated” instead of “uv” to get rid of it. Alternatively, you set the seam elsewhere an unwrap again.
With regards to your modifiers, Why do you use bevel and subsurf together? If you bevel with a tiny radius this will act as support cuts and suppress the subsurf with dead geometry at the edges. Better do either a subsurf set to “simple” if the flat appearance is intended, or bevel with a larger radius.
