Linked Server works on SSMS and isn't found on SSDT
Could you share the linked object name along with the query?
Sometimes the problem is on the FROM part. There are a lot of situations where you can get this error, and many of them are covered on StackOverflow. However, one case which might especially be encountered on shared servers is simply that the database name has a period (dot) in it. For example, if its name is mysite.com_DB. This will automatically cause the problem.

The solution, if you can't rename the database, is to encapsulate the DB name in square brackets, so for example:

mysite.com_DB.Table_name


Will turn into: 

[mysite.com_DB].Table_name