Improve differentiation between tools in different IDEs

I have the MCP server plugin enabled in RustRover and IntelliJ on different ports. The two servers are registered in Claude Desktop with a corresponding name. I gave Claude a prompt akin to "In rustrover read file xyz. Create an equivalent Java class in intellij under the directory foobar". Claude executed the request I gave it correctly, but it didn't write the output using the appropriate intellij MCP tool. Instead it used the rustrover variant.

It seems like the name of the MCP server does not play a significant role in tool selection. That would make sense since the MCP server name isn't really part of the MCP protocol. Would it make sense to extend the names and/or descriptions of the tools with the name of the IDE running the MCP server? That might make tool selection work more reliably.