The owners of the key pair whose public half you are tricked into using get to see the otherwise concealed ClientHello which today includes SNI and ALPN. So e.g. they'd know you wanted to speak HTTP/2 to some.name.example

But on the other hand to have substituted this key for the correct one they presumably already intercepted your DNS query and so they likely already knew you were intending to talk to some.name.example from that query.