Domain name and speed

I would like to ask if there can be any affect on speed of download time for my website caused by "provider" of my domain name.

Lets say, I have good hosting plan for my website, but I bought domain name from another provider.
Now that domain name is "parked" on my hosting server.

I am just curious if I should be careful when looking for provider of domain the same way like with hosting?

Thanks =)