Repairing buggy query server-side – without changes in the app
You are facing the error Ambiguous column name… because the app is quering your database this way:
SELECT 
[Name], 
[Salary], 
[Name], 
[Age]
FROM TABLE1 A 
INNER JOIN TABLE2 B 
ON A.EmployeeID = B.EmployeeID

As you can see there are two [Name] in the SELECT. You will resolve the issue by recreating the query this way:
SELECT 
A.[Name], 
[Salary], 
B.[Name], 
[Age]
FROM TABLE1 A 
INNER JOIN TABLE2 B 
ON A.EmployeeID = B.EmployeeID

Yes, you are facing this because, as you said, you are adding some columns in your DB. You have 2 choices:

Contact the vendor and make it aware of the Ambiguous column name… error
Recreate the structure of your database and avoid using column names that were already used.