can you provide a bit more of a background on why exactly do you need leads to write the real legal name? Then it'd be easier to come up with a helpful suggestion.
But in general, its very difficult to set up 100% bulletproof system; there is a similar challenge (or never ending story) on requiring business email addresses in forms. You can try a combination of hints/hover-on instructions and see if it helps. Or create a smart campaign/autoresponder email to explain leads its important to provide real names and call them to confirm/adjust their provided info.
Hope it helps.
I don't think it's intimidating to use the word "legal," as long as you ground it in the nature of your business (I assume it has something to do with public records?) and your language is otherwise informal.
In addition to descriptive text on the form, you can try a confirmation popup when they hit Submit that repeats the rule: "Please confirm that you've provided your full legal name" with Confirm and Go Back/Edit options.
But like Matjaž says, if you don't have the force of actual law behind you, you can't really force people to do anything on a form.
How about showing them that one field is for their First Name and have another one that is for their Nickname? I've seen this a lot. It may spur people to know that if their name is say William that they will then put William in as their First name and Will/Bill for their nickname? It's worth testing at least. You can have the nickname as a Marketo custom field and then use that when you personalize their emails.
Just a thought