Support customizing clientInfo when connecting to MCP servers

[atinylittleshell]

Description

Currently there's no way to customize clientInfo.name when connecting to MCP servers, which limits the ability for the agent to identify itself to the server.

See reference below - it would be good to have support for it.

References

https://modelcontextprotocol.io/specification/2025-06-18/basic/lifecycle#initialization

[DouweM]

@atinylittleshell Makes sense, PR welcome!

[atinylittleshell]

@DouweM here you go :) let me know if you'd like me to tweak anything there