When asking a question like this, think of how you would answer the question.

Correct:

[What do you think] [my name is]?

The answer is, "[My name is] Keiki."

[How do you think] [it is done]?

The answer is, "[It is done] like this."

[Does anyone remember how] [we connected to the server]?

The answer is, "[We connected to the server] like this."

Incorrect:

[What do you think] [is my name]?

"[Is my name] Keiki," is another question, not an answer.

[How do you think] [is it done]?

"[Is it done] like this," is another question, not an answer.

[Does anyone remember how] [did we connect to the server]?

"[Did we connect to the server] like this," is another question, not an answer.

I can't tell you the technical term for why this is correct, and like all rules, there are probably exceptions, but I think it's pretty easy to remember like this.

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)