Hi RichardSa,
1. In Visual Studio go to Tools -> Connect to Database.
2. Under Server Name Select your Database Server Name.
3. Under Connect to a Database, Select or enter a database name.
4. Select your Database from Dropdown.
5. After selecting Database try Test Connection.
6. If Test Connection Succeeds, Click Ok.
7. In Visual Studio go to View -> Server Explorer.
8. In Server Explorer window, Under Data Connections Select your Database. Right Click your Database -> Click Properties.
9. In Properties window you will see your Connection String.
Refer
https://www.c-sharpcorner.com/UploadFile/d40a40/get-sql-server-database-connection-string-easily-from-visual/