Brokerkit starts every text conversation with a message containing all the lead's contact information, so you always know who you're talking to.
If you ever can't find that first text, reply to the text from Brokerkit with ?who and the info text will be resent. And no worries - this won't be sent to the lead.
You can also use the Engagement filter in the user interface to search for text replies in the last 7 or 30 days and reply to them in the contact profile. See here for details.