First step to change page title it is to understand where title string is stored. Easiest way to do that is to open the default.aspx page with Sharepoint Designer. We can see it contains a content block that replaces the master page's Title content placeholder.

Here is the master page extract:

<Title ID=onetidTitle><asp:ContentPlaceHolder id=PlaceHolderPageTitle runat="server"/></Title>

And here is the replacement in default.aspx:

<asp:Content ContentPlaceHolderId="PlaceHolderPageTitle" runat="server">
 <SharePoint:EncodedLiteral runat="server" text="<%$Resources:wss,multipages_homelink_text%>" 
       EncodeMethod="HtmlEncode"/> - 
 <SharePoint:ProjectProperty Property="Title" runat="server"/>
</asp:Content>

We can see that the title is made up of two parts, the localized "Home" string and the current site's name taken from the site's properties. We have two options here - we can either find the resource string and change it, or remove it from the ASPX altogether (along with the connecting dash) and have a clean page title. The second option is pretty straightforward, so we'll focus on the first:

text="<%$Resources:wss,multipages_homelink_text%>" 

We can see that the actual text is retrieved from some Resource Manager. The format of the $Resources token is as follows:

$Resources:filename,localizedString

So what we need is the string "multipages_homelink_text" under the file wss.resx or wss.en-US.resx. You can find it under C:\inetpub\wwwroot\wss\VirtualDirectories\<port>\App_GlobalResources. Just change its value there and it will be instantly update the site, no IISRESET necessary.