We have two Cosmos connectors with very long names: AzureCosmosDBMongoDB and AzureCosmosDBNoSQL; this forces the user to deal with type names such as AzureCosmosDBMongoDBVectorStoreRecordCollection.

• The official Cosmos SDK doesn't include Azure in type names (e.g. CosmosClient), and AFAICT packages targeting Cosmos don't include Azure in their namespace or package names (e.g. EF Core's Microsoft.EntityFrameworkCore.Cosmos).
• The same is true of the DB suffix: although the full marketing product name is CosmosDB, on APIs the DB is omitted; Cosmos seems to be generally sufficient.
• Similarly, on the Mongo side, the DB suffix is omitted on type names, e.g. the client is just called MongoClient, and not MongoDBClient.

As a result, I propose renaming the packages to Microsoft.SemanticKernel.Connectors.CosmosNoSQL and CosmosMongoDB. Type names within the package can be called e.g. CosmosNoSQLVectorStoreRecordCollection and CosmosMongoVectorStoreRecordCollection (I plan to propose further possible simplifications to the VectorStoreRecordCollection to make this a bit shorter still).