The correct name of the service is eduroam, all lower case. No other form should be used: "Eduroam", "EduRoam", "edu-roam", "EDU-ROAM" and other variants are all incorrect. Whilst it might seem contrary to normal English use, the term eduroam should never be capitalised (even at the beginning of a sentence).
This might seem like a trivial and pedantic issue, but it turns out to be surprisingly important. Wireless network names are case sensitive, and so "Eduroam" is not the same wireless network as "eduroam". To avoid confusing users we'd like any other mention of eduroam (e.g. in correspondence and documentation) to be consistent with the wireless network name.
It might not be obvious, but there is an underlying security issue that affects your users. Anybody can bring up a wireless network with any name, and so one of the risks with a widely-adopted service like eduroam is that a malicious person publishes an "eduroam" (or "Eduroam" or equivalent) wireless network and tries to phish accounts by convincing users to log in with a captive portal (this is the subject of a security advisory). There have been reported attempts in the past of attackers using case variations in a place where eduroam may normally available in an attempt to coerce people to join their network. This is why it's vitally important that we strongly reinforce consistent capitalisation for end users of the service.
eduroam is a registered trademark in South Africa and abroad, meaning that malicious uses like the above can still be prosecuted under trademark law even when it might otherwise be difficult to prove the attack. This is one of the legal tools available to protect the service. However, brand consistency is important in cases like this. Thus the correct capitalisation is an issue both the South African NRO and the global eduroam governing body feel very strongly about.
If you are the eduroam contact for an institution, please make sure your help desk are aware of this and review and documentation you've made available to users to check the capitalisation. Likewise, if you notice any incorrect capitalisation on this website, please let us know!