My research into this area has uncovered a few options. The US forestry service has a number of tools called i-Tree that might help, https://www.itreetools.org/ Click on tools and check out i-Tree Eco. You will need to download the program. Eco allows you to create an inventory and define the fields you want. In addition to GPS you can record size, crown health, etc. Another tool called My Tree will allow you to record the trees on your property to determine the value they have for energy reduction, water runoff avoided, carbon capture, etc. It's not an inventory, but cool. The Design module can help you plan future plantings, and Species can help you select trees based on some variables.
I have also used Google Maps to save locations. locate a point on the map and click on Save. It will give you an option to save to Favorites, Want To Go, or create a new list. I haven't tried it, but you can stand under the tree, click on the location in Maps and then save it. Drop a pin, click on the GPS coordinates and save it. You can add a label to describe the tree.
Hope this helps. Let me know what you think.
Q