Since you've referenced CLDR already, I may be saying things you know, and you're looking for an "official position" from IANA folks. If so, please feel free to ignore the info below, I'm mostly just a lurker here who has been straddling a few different libraries for Android for a few years, so I appreciate some of the terminology / disconnects.
Below I'll refer to identifiers like "Europe/London" as the zone ID. I think the TZDB nomenclature uses "zone name" for this, but I tend to avoid it because it's confusing in the Java / ICU world when also talking about "display names".
Somebody who knows better will be along to correct me, but I think strings like 'Central European Summer Time' are obtained in CLDR / ICU internals via the "metazone" mapping, which CLDR originates.
i.e. zone IDs that share the same "Central European Summer Time" string at a given point in time are in the same metazone at that time. Zone IDs that have the same offset + rules according to TZDB, even in the same country, may have different metazones because the populace may choose to call their time something different even if they follow the same rules right now. Across borders, two neighboring countries that share the same rules may also choose to observe the same naming (e.g. the EU may like Central European Time) or different (e.g. "Irish Standard Time" / "British Summer Time"). Because names have geopolitical implications, this can get a bit complicated (e.g. Crimea), which is why I'm glad CLDR looks after it. CLDR also specifies times when a zone ID is in a metazone, so a given zone ID that may be in one metazone today may be in a different metazone tomorrow (e.g. Yukon changes last year, IIRC).
All that said, metazones could perhaps be ignored as an implementation detail used to derive a name for a zone ID. I tend to refer to names like 'Central European Summer Time' as the (long) "display name". This is because I first encountered these via ICU and Java APIs which use the TimeZone getDisplayName method to obtain them and have constants for long ("Mountain Daylight Time") / short ("MDT") / generic long ("Mountain Time"), etc.
Hope that helps,
Neil.