Single SMS button feature can be configured for all objects like Contact, Account or to any custom object.
ValueText AppExchange package installation will enable you to have Send SMS or Bulk SMS button for contacts, accounts, case, lead & opportunity object. You may have to drag that button from page layout to make it available for users.
How To: Create SMS button for Custom Object :
Log into salesforce > setup > Create > Objects > select object which you want to create a button > at “buttons, Links and Actions” section click on “New Button or Link”.
Like below image, mark “Detail Page Button” , Behavior as “Display in new window ” and Content Source as “URL”.
Copy and paste the below code in the formula window
Replace “ObjectAPI-Name” with custom object API name. For Example: for a contact object, “Contact” and click on Save button.
Once saved, you need to drag the button from page layout for user access.