Advantages of wedge/forum: better URL, and if you fork the project, your repo's description has 'forked from Wedge/forum' in it. It's descriptive.
Drawbacks: if someone forks your fork, nowhere can you see that it's a fork of Wedge.
Advantages of wedge/wedge: see above. Drawbacks: it's repetitive, repetitive. But it's the convention around software built from an organization repo (phpbb/phpbb, mybb/mybb...)
Advantages of wedge over Wedge: none, it's just a matter of taste.
Choosing one of these isn't a big deal, but once it's chosen, I can't change it anymore. (Except for the casing in the organization name. But that's all.)
Drawbacks: if someone forks your fork, nowhere can you see that it's a fork of Wedge.
Advantages of wedge/wedge: see above. Drawbacks: it's repetitive, repetitive. But it's the convention around software built from an organization repo (phpbb/phpbb, mybb/mybb...)
Advantages of wedge over Wedge: none, it's just a matter of taste.
Choosing one of these isn't a big deal, but once it's chosen, I can't change it anymore. (Except for the casing in the organization name. But that's all.)