The default vector search index name in Compass is "default" and "vector_index" in the Atlas UI.
I think it should be consistent and be "vector_index" across both as it is a clearer name.
As someone who helps write or tech review a lot of internal and guest author tutorials on Vector Search, it is too easy to face issues if racing through the creation wizard, or accidentally using terms like "you can use the default value for the name". This can lead to issues later on because code snippets referencing the default value might differ and error depending on what was used