Do Not Use a Comma After Dear
There is no comma after the word Dear when it is used at the start of a letter or an email. You should, however, use a comma after the salutation. For example:
Thanks for paying for dinner last night.
Thank you for your comments on Apollo 11.
In very formal circumstances, you could follow your salutation with a colon. For example:
I regret to inform you that your application has been declined.
Thank you once again for hosting our discussion.
The word Dear is an adjective. It describes the noun it precedes. Putting a comma after Dear would be as bad as putting one after red in red bus.
A Comma with Hi or Hello
When the salutation in your letter or email starts with Hello or Hi, then you should put a comma before the name of the person you're addressing. It is also standard practice to put a comma after the name of the person you're addressing. For example:
Thanks for paying for dinner last night.
Thank you for your comments on Apollo 11.
Using a colon (instead of a comma) after such an informal salutation would not be an error, but it would be unusual. You could also use an exclamation mark if you wanted to emphasize an emotion (like surprise).
It's All About the Vocative Case
In English, when you address someone (or something) directly, the name you use is offset with a comma (if it's at the very start or end of the sentence) or two commas (if it's in the middle ). When you address someone directly, their name is said to be in the vocative case. In the examples below, the words in the vocative case are shaded:
Thanks for paying for dinner last night.
Thanks for paying for dinner last night.