scrawl
To write in a messy, rushed way that’s hard to read.
Scrawl means to write quickly and carelessly, producing messy, hard-to-read handwriting. When you scrawl your name on a sign-up sheet while rushing to recess, the letters might come out crooked and jumbled. A doctor famously scrawls a prescription so hastily that pharmacists struggle to read it.
The word captures both the action and the result. You can scrawl a note (the verb), or you can look at someone's messy scrawl (the noun) and wonder what it says. Scrawl suggests impatience or hurry: someone who scrawls isn't taking time to form neat letters.
Compare scrawl to scribble, which means writing or drawing carelessly. Scrawl specifically refers to messy writing, while scribble can describe any careless marks on paper. When your little sister scribbles on your homework with crayon, she's not scrawling because she's not forming letters or words.
The handwriting itself might be called a scrawl: “I could barely read his scrawl across the birthday card.” While neat handwriting shows care and consideration for your reader, a scrawl suggests you were in too much of a rush to make your words easy to read.