I am trying to connect My R studio to SQL Database on the Remote Desktop
Basically, when you failed to connect to your SQL Server, the issue could be:


Network issue. SQL Server configuration issue. 
Firewall issue.
Client driver issue.
Application configuration issue.
Authentication
    and logon issue.


Check this link for more details.

In your error message it is just a login failure:


  Login failed for user 'HMINDIA\274074'


you need to create a login.
there are windows logins and sql logins:

for example (windows login - attached to the active directory):

USE [master]
GO

CREATE LOGIN [my_domain\my_login] 
FROM WINDOWS WITH DEFAULT_DATABASE=[master], DEFAULT_LANGUAGE=[us_english]
GO

--grant the access and permissions accordingly
--in this case it is a sysadmin
--ALTER SERVER ROLE [sysadmin] ADD MEMBER [my_domain\my_login]
GO


example of creating a sql login:

USE [master]
GO


CREATE LOGIN [my_ETL_login] WITH PASSWORD=N'Hare_Krishna108', 
DEFAULT_DATABASE=[master], 
DEFAULT_LANGUAGE=[us_english], 
CHECK_EXPIRATION=OFF, CHECK_POLICY=OFF
GO

-- grant access to this login
-- this login will be able to access and read database CAMemeMail:

    USE [CAMemeMail]
    GO
    CREATE USER [my_ETL_login] FOR LOGIN [my_ETL_login]
    GO
    USE [CAMemeMail]
    GO
    ALTER USER [my_ETL_login] WITH DEFAULT_SCHEMA=[dbo]
    GO
    USE [CAMemeMail]
    GO
    ALTER ROLE [db_datareader] ADD MEMBER [my_ETL_login]
    GO


And don't forget the firewall