error CS0103: The name ' ' does not exist in the current context

Simply move the declaration outside of the if block.

@{
string currentstore=HttpContext.Current.Request.ServerVariables["HTTP_HOST"];
string imgsrc="";
if (currentstore == "www.mydomain.com")
    {
    <link href="/path/to/my/stylesheets/styles1-print.css" rel="stylesheet" type="text/css" />
    imgsrc="/content/images/uploaded/store1_logo.jpg";
    }
else
    {
    <link href="/path/to/my/stylesheets/styles2-print.css" rel="stylesheet" type="text/css" />
    imgsrc="/content/images/uploaded/store2_logo.gif";
    }
}

<a href="@Url.RouteUrl("HomePage")" class="logo"><img  alt="" src="@imgsrc"></a>

You could make it a bit cleaner.

@{
string currentstore=HttpContext.Current.Request.ServerVariables["HTTP_HOST"];
string imgsrc="/content/images/uploaded/store2_logo.gif";
if (currentstore == "www.mydomain.com")
    {
    <link href="/path/to/my/stylesheets/styles1-print.css" rel="stylesheet" type="text/css" />
    imgsrc="/content/images/uploaded/store1_logo.jpg";
    }
else
    {
    <link href="/path/to/my/stylesheets/styles2-print.css" rel="stylesheet" type="text/css" />
    }
}