A serious locksmith will want to know from you whether you are authorised to access the house or apartment. So it's OK if the locksmith asks for the address in your ID.
Second: Ask for a price!
Here, it is once again important to remain calm. You should tell the locksmith in as much detail as possible what happened. Is the door just closed or locked? Usually it is enough just to open the door again. Say what needs to be done to avoid unnecessary costs. For example, the replacement of an entire lock. With this information, a reputable locksmith service provider can tell you the estimated total cost - including travel costs and hourly rates.