It makes no difference how many dots you include in your Gmail address or how you capitalize it.
It would seem like common sense – if your Gmail address is Test.firstname.lastname@example.org, the dot between your first and last name and the way in which your name is capitalized should uniquely identify you to rest of the emailing public. But, then again, everything is relative – in space-time and in Gmail accounts.
In fact, the dots in your Gmail address are meaningless and are completely ignored. The same goes for capitalization. To put it in perspective, every one of the following emails will end up in the same Gmail account’s inbox:
The dots and capitalization can help make the Gmail address easier to read for humans, but the Google Gmail servers don’t even notice them.