A few notes about product names.
Shortening Google product names
When referring to a Google product, sometimes you might want to abbreviate the product name. For example, when you're referring to Google Spreadsheets, it can be awkward to refer to it as Google Spreadsheets every time; sometimes you might want to call it Spreadsheets.
Use the full trademarked product name whenever possible. In particular, use it the first time the product is mentioned on the page, and in the document title and headings, and wherever it's especially prominent.
However, in some contexts, space or aesthetic considerations demand shortening in less-prominent instances of the product name. That's okay, as long as you continue to make clear that you're talking about the Google product and not some other thing with a similar name.
If you use a product name as a modifier, pay close attention to which article precedes the product name. For example, consider Anthos Service Mesh (the long name) and Service Mesh (the short name). You would write an Anthos Service Mesh environment, but a Service Mesh environment.
Possessives of product names
For information about forming possessives with product names, see Company- and product-name possessives.
Using "the" with product names
Don't use "the" before a product name unless you're using the name to qualify something else. Do use "the" before tool and API names.
Not recommended: Using the Cloud Datastore with Cloud Dataproc
Recommended: Using Cloud Datastore with Cloud Dataproc
Recommended: The Cloud Datastore options page
Recommended: The GCP Console
Recommended: The Transcoder API
It's OK to refer to Google products as services, such as the Google Kubernetes Engine service or the Compute Engine service. However, if the term services leads to ambiguity, use the product names.