How to get store name in template?

you need to use the instance of \Magento\Framework\App\Config\ScopeConfigInterface in your block:

Create the method getStoreName()

public function getStoreName()
{
    return $this->_scopeConfig->getValue(
        'general/store_information/name',
        \Magento\Store\Model\ScopeInterface::SCOPE_STORE
    );
}

and call in your template echo $this->getStoreName()

Use store manager, which holds information about active store. If custom block is not inherited from Template block, inject dependency on \Magento\Store\Model\StoreManagerInterface in construct.

<?php
namespace VendorName\ModuleName\Block;

class CustomBlock extends \Magento\Framework\View\Element\Template
{
    /**
     * Get current store name.
     *
     * @return string
     */
    public function getCurrentStoreName()
    {
        return $this->_storeManager->getStore()->getName();
    }
}

Then in template:

<?php
/**
 * @var $block \VendorName\ModuleName\Block\CustomBlock
 */
echo "<h1>Current store name is '{$block->getCurrentStoreName()}'</h1>";
?>

To get a store configuration value like general/store_information/name you can use the following

$config = new \Magento\Framework\App\Config\ScopeConfigInterface();

echo $config->getValue('general/store_information/name');

However, doing this from a block or helper would be cleaner. Below is a helper class that would exist in your own custom module

namespace [Namespace]\[Module]\Helper;

class Data extends \Magento\Framework\App\Helper\AbstractHelper
{
    /**
     * Retrieve store name
     *
     * @return string|null
     */
    public function getStoreName()
    {
        return $this->scopeConfig->getValue(
            'general/store_information/name',
            \Magento\Store\Model\ScopeInterface::SCOPE_STORE
        );
    }
}

Which you would inject as dependency in your block class