You have to use IP Address to connect to remote hosted sql server
Check here -
Data Source=190.190.200.100,1433;Network Library=DBMSSOCN;
Initial Catalog=myDataBase;User ID=myUsername;Password=myPassword;
DBMSSOCN=TCP/IP is how to use TCP/IP instead of Named Pipes. At the end of the Data Source is the port to use. 1433 is the default port for SQL Server.
More details, you can see here
http://www.connectionstrings.com/define-sql-server-network-protocol/[
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Now for hosting, contact a Sql Server Hosting Service provider and choose a plan and host a sql server. The Service provider will provide you the ipaddress and port which you will use in your connection string.
Other option (most preferable to me) is to use Microsoft Sync Framework which sync server data to your local data. This will be pretty fast and robust compared to connectiong directly through ip.
Hope this info helps!
Thanks,
Cheers