I never learned cursive (can't even read it most of the time) but I don't think my answer would be helpful to you. But it might be interesting.
My signature isn't my full name, it's just an arrangement of 3 alphanumeric symbols that has meaning to me but to anyone else probably looks like a meaningless scribble. If someone ever tries to forge my signature, they'll almost definitely do it wrong.
But the reason my answer isn't useful is that English isn't my native tongue, and neither is the Latin alphabet. My native tongue is Hebrew. Hebrew cursive is very different from Latin cursive, in that the letters don't flow into each other. It's still "block letters", just a different variant of them. I've never looked at many signatures but I think a lot of people just write their name quickly, and that inevitably involves lifting the pen from the paper between letters multiple times.
In a lot of less important contexts that require signature (e.g. receiving a package), many people just make a really quick meaningless scribble, which might look like α or φ or whatever to just get on with it. Workers asking for these signatures often humorously say "give me a scribble here" in those scenarios.