Since pyenv 2.3.6 (November 2022) it will automatically resolve a prefix version to the latest revision:
pyenv install 3.10
Note that, as the link indicates, pyenv uninstall does not do prefix resolution, it needs the full version upfront.
You may need to update your pyenv if it’s too old (pyenv -v will tell you the version of pyenv itself)
old outdated answer:
FWIW as of version 1.2.24 (March 2021) this issue is finally fixed:
pyenv install 3.10:latest
pyenv/pyenv#1831 lets you suffix any section of version with :latest (just avoid :latest alone it yields weird results) to get the latest revision for that section e.g. right now 3:latest will install 3.11 alpha, 3.10:latest will install 3.10.0.
It’s not quite perfect when dealing with non-mainline, and :latest doesn’t work in every context, but it’s progress.