How do you make sure that you are getting your domain name in a timely manner by the registrar. And how do you check to see if they have registered it in your name.

Just check registry.in and see if your contact details are on the domain

If you're dealing directly with an Indian registrar, the domain should be registered in less than a minute. Some registrars that offer Indian domains (like Moniker) are actually just agents for other registrars and it can take a few hours for the domain to be registered. I'd generally recommend dealing directly with Indian registrars instead of the middleman.

Infact almost all registrars provide the domain name immediately..it is in your name because is it under your customer account when you register it..however, you can always check in the whois records and ascertain if you indeed are the owner or not..