Issue connecting Dapps to my forked & customized version of metamask.

Hi,
I forked the Metamask wallet repo, and have been adding some features I believe will make the application even more powerful.
I'm trying to connect to my updated version of the wallet using live Dapps but they can't seem to distinguish between the two wallets, when installed on the same browser.
I believe its a provider issue, and i've been working to find a way to distinguish the wallets as separate wallets to Dapps to no avail.
[This](https://github.com/MetaMask/providers/blob/main/src/BaseProvider.ts) is the `metamask/provider` package which handles the connection by Dapps to Metamask in this file `Baseprovider.ts`.

I found the `handleConnect` function inside, but can't seem to make sense of how it handles the connection by Dapps, and how I can edit it to suit my needs.
I'm hoping someone that better understands the project can point me to what I need to change to achieve this.
I’ll really appreciate any help.
Thanks.

Start with src/BaseProvider.ts in the @metamask/provider package, especially handleConnect, and trace how the provider is identified by connected Dapps. Determine whether the provider supports distinguishing separately installed wallet forks and document the project-supported change or limitation needed for this use case.

Written by the indexing model from the issue text.