language servers: Fix wrong language server name (#20428)

This fixes the issue of multiple language servers showing up as `node`
in the language server logs dropdown.

It does this by changing `language_server.name()` to return the
adapter's name, not the binary name, and changing types to make sure
that we always use this.

Release Notes:

- Fixed language server names showing up only as `"node"`

---------

Co-authored-by: Sam Rose <hello@samwho.dev>
Co-authored-by: Bennet <bennet@zed.dev>

crates/copilot/src/copilot.rs

@@ -21,7 +21,7 @@ use language::{
     point_from_lsp, point_to_lsp, Anchor, Bias, Buffer, BufferSnapshot, Language, PointUtf16,
     ToPointUtf16,
 };
-use lsp::{LanguageServer, LanguageServerBinary, LanguageServerId};
+use lsp::{LanguageServer, LanguageServerBinary, LanguageServerId, LanguageServerName};
 use node_runtime::NodeRuntime;
 use parking_lot::Mutex;
 use request::StatusNotification;
@@ -446,9 +446,11 @@ impl Copilot {
                 Path::new("/")
             };
 
+            let server_name = LanguageServerName("copilot".into());
             let server = LanguageServer::new(
                 Arc::new(Mutex::new(None)),
                 new_server_id,
+                server_name,
                 binary,
                 root_path,
                 None,