Ygtjki

The signature on my driver's license is a unique and identifiable smiley face :-)

I use this signature to sign all legally binding documents. A lot of the time, people reject it, and request an "actual signature". I then show them that it is the same signature as my driver's license, and they usually, (but not always,) accept it.

Is my signature legal? Or must it be my name? If it is legal, is it a bad idea?

Can I sign legal documents with a smiley face?

Yes, that is lawful. A person's signature does not necessarily have to include the person's name or initials. What matters is that the signature reliably and unequivocally identifies the person who produces it, which apparently you have been able to prove by showing your driver's license.

The Black's Law Dictionary (4th Edition) states in its entry for signature that "whatever mark, symbol, or device one may choose to employ as representative of himself is sufficient". It directs to the entry for sign, which likewise speaks in terms of "any mark, as upon a document, in token of knowledge, approval, acceptance or obligation". Accordingly, your signature qualifies as mark or symbol that fits these purposes.

Your history of signing other legally binding documents that way further reinforces the authenticity of your signature.

If it is legal, is it a bad idea?

It is a bad idea to the extent (if any) that (1) others can easily forge your signature (notwithstanding that forgery or identity theft might be proved circumstantially); and (2) verifying your identity may cause hassle or annoyance to you and/or third parties. But this paragraph obviously is applicable to any and all signatures, not just those which at first glance may seem to be a joke.

A contract is a meeting of the minds. If your conduct before and immediately after the signing resembles the way people act when they have a meeting of the minds, that is proof of agreement.

To invalidate a contract over a defective signature, a party would have to object timely to the signature; immediately or the first time they reasonably should have seen it.

And then, since a contract is a meeting of the minds, you must reach a meeting of the minds about what an acceptable signature is. Both of you can draw vulgar graffiti tier art of a rooster and balls for all it matters, as long as you both signed it.

I'm not sure if this is legal in the US, because the attitude towards name and identification issues is quite different from Europe.
Where I live, only the written surname (first name optional) is considered a valid signature (in most cases). Some documents, like a Last Will, even need to be signed with your full name, including middle name(s).

It is possible though to use any sign as your legal signature if the sign is registered and affirmed by a notary. This exception was intended for people who aren't able to write.

I bet there's a similiar law in the US.