Trail Names & Trail Signs Problem

I am new to using OpenStreetMap and would like to start recording GPS tracks of some of the local hiking trails while I am doing my daily walks and bicycle rides for exercise. At first, I was thinking that I could just get the trail names from the occasional signs along the local city hiking trails. The problem is that for most of the city trails, the trail signs are just small laminated portions of the cities own printed trail maps mounted on a post. I would need to look at the small printed map on one of the signs to see the name of the trail that I am on. Would getting the name of the trail I am on from one of those posted little maps along the trail be a copyright violation?

The problem would only exist for the local City of Prescott hiking trails, not for the local Prescott National Forest hiking trails, since only the city uses small laminated maps on posts as signs. Perhaps at first, I should not include the names of the city trails on the information that I collect.

Could I avoid copyright concerns if I were to show a printed out portion of an updated version of the OSM map to the City of Prescott trails specialist, and then ask him what the names are? He is the Parks and Recreation Department employee who has been in charge of creating most of the new trails. Perhaps, I could also show the updated version of the OSM map to members of the local group of volunteers who helped build most of those trails, and ask them what the names are. Chris and the Over the Hill Gang volunteers helped layout and build most of those new trails, and were probably the ones who named the trails. Most likely, they could tell me the names of all the new city trails from memory. Would I need to somehow document that their knowledge was where I got the trail names?

Is there a better solution for getting the names of the hiking trails that I have not thought of?

I am waiting for UPS to bring the GPS that I ordered, so that I can get started soon. I am new to using OpenStreetMap and am just now reading the Beginners Guide and am waiting to get started. The majority of the many local hiking trails are not yet on your map. This is up in the mountains in Arizona here in the U.S. by the way.