When you change your name and do not leave ties back to your old name, it is difficult for a police officer to cite you with giving a false name. If the police officer only knows the name of the new man, he cannot say that the name you gave him is false. He must have evidence that you have used another name. If the officer checks their criminal records and cannot trace you back to the old man - he will probably not cite you with giving a false name.
One way the police trace you is by the Vehicle Identification Number (VIN) on the vehicle. If the vehicle you are driving was previously registered with the state in the old man's name, they may make the tie. The state-registered owner was also age 40, 6 feet tall and weighs 180 pounds. It sounds like a description of you, so they'll assume it is you.
The state records are in the old man's name. The state motor vehicles division has no court orders saying you changed your name. Therefore, they assume the worst - that you are lying about your name. Also, if you have had previous encounters with the local police and they know your old name, they will probably charge you with giving a false name.
Even though "giving false name" is an easy charge to overcome, you can take preventive measures to avoid the charge: