DL was NOT provided or used as ID

[allodial]

There are a variety of ways to deal with the signature line. If at a loss for space...

John Henry for the parties
John Henry for the driver
John Henry as Secured Party
John Henry as Claimant
John Henry as Agent

[ Believe it or not Doe is left out on purpose! ]

The following require more space:

John Henry for DOE JOHN H
John Henry for the State of California
John Henry d/b/a DOE JOHN H

I know of someone that has established that its, say,

House of Smith d/b/a
DOE JOHN H...

This was established by letterhead sent to the head of the DMV or the like.

If there is really a severe space restriction for 'signature', one could simply put:

DOE JOHN H
or
DOE JOHN H 1293993 {license or ID #}

Either way, one can within three days or so of filling out the app for a DL send a letter to the DMV (Director or Attorney) or SoS that might go along these lines:

John Henry of the Doe clan

To fiduciary agents/officers of the DMV:

This is to inform you that I, __________________, on behalf of

DOE JOHN H

and/or for

JOHN HENRY DOE
(CALIFORNIA) File # ______________

apply for {or renew or whatever} a CALIFORNIA IDENTIFICATION CARD.

I would not suggest a "true name" signature. True Name d/b/a ENTITY #3049494 is one thing. But merely signing True Name could put you in the position of accommodation party. IMHO its best to just put

DOE JOHN H #03949494
or
DOE JOHN H

for the signature if you are extremely pressed for space and to always subsequently notify the DMV of your power of attorney or some other claim---IN OTHER WORDS make it clear as pie without a bunch of blah blah blah Paytriot kitchen sinkage that John Henry was acting as Attorney-In-Fact in putting the signature of the ENTITY on the signature pad--as in so they cant presume otherwise. Alternatively or additionally one could file a fictitious name registration that shows say...

John Henry, c/o private 100 Main street, New York, New York not domestic

doing business as DOE JOHN H

Don't expect the lemming mindset to even remotely comprehend your exercise of brains. If you are having conceptual issues perhaps you are suffering from Stockholm Syndrome.