In Intellij Idea I can see documentation on intelliSense options:
Can I enable something like this in vs code for golang ? Can I control the width and height of the two rectangles ?
Try installing the Go extension. Here's the source: https://github.com/Microsoft/vscode-go
It offers Intellisense/completion lists, though the completion lists feature is not working too well right now (I'm sure it will improve over time). The extension is able to get function signatures and documentation by mousing over their names once you've typed them in, even if they don't show up in Intellisense, however.
Be sure to read the extension documentation on how to get everything installed, as it makes use of a number of tools to offer all of its functionality.