Question: So, instead of naming a link to index page a "Home" and such, how about using a domain name or the most important keyword the homepage ranks for? The link anchor "Home" definitely doesn't strengthen any ranks SEO wise as it is not informative.

What is the best way of naming the sitewide link anchor of a home page?

Answer: 
In the past I had a small site to which the anchor text to the homepage (index page in your case) was a keyword, and not "home". It worked quite well in terms of ranking on Google. But in my case, the homepage was a long page with content, and it was one of the main pages of the site (small site).

I'm not sure how your homepage looks like. If the homepage just directs users to other pages, then you better try to use your keyword in question on an anchor that sends user to a specific content page, relevant to that specific keyword. 

The best and default answer would be - use microformats of `rel="home"` inside the anchor tag , and use "home" as the anchor text. This makes navigation clearer for your users, and clear navigation is one of the signals of google for quality.
As a sidenote, while on the subject of SEO and homepage links. Are you considering whether the address used to access your homepage is consistent? A lot of webmasters make the mistake of serving their homepage at example.com/ but linking to example.com/index.php from deeper pages. Googlebot will consider these 2 different pages and report duplicate content. Duplicate content reduces quality score. Always make your home button in your navigation link to `/` 

**Good Example (Consistent addresses on Home links):**

```
<nav><a href="/">Home</a> | <a href="/FAQ">FAQ</a></nav>
<main>
    <p>As you may have read on the <a href="/">Homepage</a> I have nice hair</p>
</main>

```

**Bad Example (Inconsistent addresses on Home link):**

```
<nav><a href="/index.php">Home</a> | <a href="/FAQ">FAQ</a></nav>
<main>
    <p>As you may have read on the <a href="/">Homepage</a> I have nice hair</p>
</main>

```