You can define & specify Mobile Number fields in Conversation view visual-force page so that it should not show up unnecessary fields while sending out SMS from Conversation view.

Please follow below steps to do the same-:

  1.  Go to 'Edit Layout' from the record of the object on which the Conversation view is built to check the Visual-force page name getting used (Name will let you the Visual-force page name )-:


   2. Go to Setup -> Enter VisualForce Page in Quick Find box -> Click on ‘Visual-force pages.’

   3. On the Visual-force pages list,  Search for Visual-force page name you found in step 1 above.

   4. Click on "Edit" against that Visual-force page

   5. In the script (next to mobileFields:) please add the API names of the phone fields that you would want to see, in the conversation        view drop down, within the double inverted comas and 'Save'. Please check below screen-shot for more detail-:


   6. To add more mobile field, add the API names separated by semicolon (;) . Eg:  MobilePhone;Phone

Now if you go to the 'Object' at the record level 'Conversation View' you will see only those phone fields that you chose.

Click Here to go through video tutorial of the same.