Well, Robin Hood was supposed to have been running around in the 12th century, so I suppose it was a bit ahistorical in the context of the guy anyway.

I think it's called the Robin Hood Tree because it was in a Robin Hood film.

If they move quickly on it, I imagine that they could probably use cuttings from the existing tree

That'd be a nice touch, from one tree dozens could spring up. Seems fitting.

Hmm. I was wondering if the National Trust would object to plantings -- I dunno if you can do that in national forests here in the US -- but it looks like they do plant stuff:

https://www.nationaltrust.org.uk/support-us/plant-a-tree

Help plant more trees

For only £5, you can plant a tree that will tackle climate change and support life for years to come. Your support will help to plant and establish 20 million trees by 2030.

1,000,000 saplings have been planted so far thanks to your donations
14 species of tree have been planted including oak, beech and crab apple

https://www.theguardian.com/environment/2022/nov/03/national-trust-to-plant-1200-hectares-of-flower-filled-grassland-in-devon

National Trust to plant 1,200 hectares of flower-filled grassland in Devon

EDIT: Looks like we do it in the US too, and the program even has the same name:

https://plantatree.fs.usda.gov/

Donations to Plant-A-Tree will be used to plant trees on national forests throughout the U.S. and territories. You can select to have your donation go to where it’s needed most or to a specific national forest. Donations to where it’s needed most are received in the national office over the course of the year and are pooled and distributed annually to reforestation projects at various locations in the national forest system.