Ability to setup messaging from custom objects is available version 4.129 onwards
Now Twilio for Salesforce allows you to do 1:1 messaging from Opportunity & from any custom object
For this example, we will setup 1:1 messaging on the opportunity object.
But you can do this for any object in Salesforce
Go to the record page and click Edit Page
Drag n Drop Twilio - Two Way Messages on your desired position in the page, and Activate & Save it
Go to Setup -> Object manager -> Twilio message -> Fields & relationships -> Click New
Select Datatype as Lookup Relationship and Click Next
Select the custom object, Opportunity in our case and Click next
Provide a name, set visibility in next screens and Save
This will connect our Twilio Message object to the custom object.
Go to Object manager -> Opportunity ->Fields & relationships -> Click New
Go to the custom object record page(we will go to Opportunity record for this example) and find the 1:1 messaging component
You can now send and receive messages from the custom object