Create variable and use in one stored procedure
You can make it shorter by having a single query, thus avoiding the extra variable @SiteIDOriginal and possibly make it a little faster:

ALTER FUNCTION [dbo].[GetImage]
(
    -- Add the parameters for the function here
    @SiteID varchar(100)
)
-- It is required as it specifies return value type
RETURNS varchar(100)
AS
BEGIN
    DECLARE @SiteImage varchar(100) = (
        SELECT ImageName
        FROM TblImages Img 
            JOIN TblPropertyDetails PD ON PD.ClientsSiteID = Img.SiteID 
        WHERE PD.ClientsSiteID = @SiteID
    ) 

    RETURN @SiteImage
END
GO


Other than that, something more of aesthetics:


try to have uniform formatting (blanks between variables and operators etc.)
use indentation (I usually treat SQL as Java or C# code where every "begin"
and "end" trigger a new level of indentation). This is particularly useful when reading rather large objects.