user99: UPDATE: After a further review in March 2017, TLG have confirmed that they would like us to change the site name. This post is kept for reference.

I've got this comment from Jan Beyer, Community Operations Manager for the LEGO Group:

Regarding the website - it should not be called LEGO Answers - this imply that the LEGO Group answers but perhaps "Answers regarding LEGO bricks".

Now I have to admit I can't really find the part of the site which says "LEGO Answers", as everywhere I look I see "LEGO® — Stack Exchange" which may be OK; but if it does exist, can it be changed somehow?

Edit to add:
The site still has <title>LEGO® - Stack Exchange</title>, and so appears as "LEGO® - Stack Exchange" in Google results, and the mobile site also still has the main page heading as "LEGO®"

Follow-up:
LEGO Legal Affairs reviewed LEGO Answers and did not cite any problems with the name. They made a few suggestions about improving the site description to bring it into compliance. So, unless we hear otherwise, the site name does not need to be changed. 

user178: Bricks
clean, simple, vague, open-ended.

user178: Brick Stack
Sort of associates itself with the stack exchange network

user4: This isn't really a crowd-sourcing type of situation. We will talk to the folks over at LEGO® to see what, if anything, needs to be done to bring the site into compliance. But we're not really in search of a branded or customized name apart from LEGO® Bricks or LEGO® <something>… whatever will bring the trademark use into compliance.

user99: Well, to this specific questions, Jan answered:

I would like to see anything without LEGO.

So there. I'm in favour of "Brick (anything)". Even "overflow", while an in-joke, has a nice ring to it - who wouldn't be like to be overflown by bricks?

user47: Brick Overflow
This has been brought up time and time again. The main reason for not calling the site Brick Overflow is that it's an in joke, and people who don't know about Stack Overflow will be confused, and hence not participate on the site, or something.
I disagree, I think it has a clear meaning in context to the site ("I have so many brick-related toys that they're overflowing everywhere!"). If you do know about Stack Overflow, there's an added bonus. Serenity was a great film, and I have friends who enjoyed watching it who had no idea Firefly existed. It still made sense on its own.

99: <p><strong>UPDATE:</strong> After a further review in March 2017, TLG have confirmed that they <a href="https://bricks.meta.stackexchange.com/q/380/">would like us to change the site name</a>. This post is kept for reference.</p>

<hr>

<p>I've got this comment from Jan Beyer, Community Operations Manager for the LEGO Group:</p>

<blockquote>
  <p>Regarding the website - it should not be called LEGO Answers - this imply that the LEGO Group answers but perhaps "Answers regarding LEGO bricks".</p>
</blockquote>

<p>Now I have to admit I can't really find the part of the site which says "LEGO Answers", as everywhere I look I see "LEGO® — Stack Exchange" which may be OK; but if it does exist, can it be changed somehow?</p>

<hr>

<p>Edit to add:</p>

<p>The site still has <code>&lt;title&gt;LEGO® - Stack Exchange&lt;/title&gt;</code>, and so appears as "LEGO® - Stack Exchange" in Google results, and the mobile site also still has the main page heading as "LEGO®"</p>

<hr>

<p>Follow-up:</p>

<p>LEGO Legal Affairs reviewed LEGO Answers and did not cite any problems with the name. They made a few suggestions about improving the site description to bring it into compliance. So, unless we hear otherwise, the site name does not need to be changed. </p>
 178: <p><strong>Bricks</strong></p>

<p>clean, simple, vague, open-ended.</p>
 178: <p><strong>Brick Stack</strong></p>

<p>Sort of associates itself with the stack exchange network</p>
 4: <p>This isn't really a crowd-sourcing type of situation. We will talk to the folks over at LEGO&reg; to see what, if anything, needs to be done to bring the site into compliance. But we're not really in search of a branded or customized name apart from LEGO&reg; Bricks or LEGO&reg; &lt;something>&hellip; whatever will bring the trademark use into compliance.</p>
 99: <p>Well, to this specific questions, Jan answered:</p>

<blockquote>
  <p>I would like to see anything without LEGO.</p>
</blockquote>

<p>So there. I'm in favour of "Brick (anything)". Even "overflow", while an in-joke, has a nice ring to it - who wouldn't be like to be overflown by bricks?</p>
 47: <h1>Brick Overflow</h1>
<p>This has been brought up time and time again. The main reason for <em><strong>not</strong></em> calling the site <strong>Brick Overflow</strong> is that it's an in joke, and people who don't know about Stack Overflow will be confused, and hence not participate on the site, or something.</p>
<p>I disagree, I think it has a clear meaning in context to the site (&quot;<em>I have so many brick-related toys that they're overflowing everywhere!</em>&quot;). If you <em>do</em> know about Stack Overflow, there's an added bonus. Serenity was a great film, and I have friends who enjoyed watching it who <em>had no idea Firefly existed</em>. It still made sense on its own.</p>
