Let's consider your first sentence -
Changing it into assertive sentence it looks like this -
You think Tom is my name.
what is the substitute of Tom.
You think what is my name.
Now change it into interrogative sentence -
What do you think is my name?
Another way to say this sentence is -
You think my name is Tom.
You think my name is what.
Now changing it into interrogative sentence -
What do you think my name is? (In my opinion this is better)
[Name are usually not people, so it's what, not who.]
Consider your second sentence - (Changing it into assertive sentence)
You think it is done in a careful way.
how is the substitute of in a careful way
You think it is done how.
Inverting subject-verb to form a question -
How do you think it is done?
I think the following sentence is wrong -
*How do you think is it done? (INCORRECT)
Your third sentence. Changing it into assertive sentence -
Anyone remembers we connected to the server in a difficult way.
Forming question -
Does anyone remember how we connected to the server?
The following sentence is incorrect -
*Does anyone remember how did we connect to the server? (INCORRECT)