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In what way can a merchant create a payment address that will gain reputation of trust (this address or some information connecting with the payment request will gain reputation over time and will be known as connected to the merchant ) but still maintain the privacy of the customers sending bitcoin to as if it acted as a new address each payment request ?

Could it be achieved with HD wallet mechanism and how ?

Could it be achieved at all ?

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Stealth Address is the answer.

Adapted from CryptoNote technology by Peter Todd (I think), Stealth Address basically is a form of Diffie-Hellman key exchange that allows sender to create a one-time key pair that only receiver can derive the private key. Thus Stealth Address allows merchant to public their well-known address while prevent any payments to be link to that address.

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    Stealth addresses predate CryptoNote (but not the fake backdating in the whitepaper). – Anonymous Sep 9 '15 at 12:18
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Another way to achieve merchant reputation of trust is to add your corporate logo over top of a QRcode containing your hot wallet address. In this case your company branding and reputation determines trust efficacy, which can increase over time. This may be achieved in tandem with Phuong Gwen's answer.

Unlike barcodes, QRcodes have ten levels of error correction and their general redundant design feature allows one to substantially modify the QRcode, for example by adding a full color company logo, while still maintaining content integrity of your wallet address.

This is a simple example of a KittyBitcoin logo superimposed in a QRcode over a bitcoin wallet address: http://kittybitcoin.com/tip.php

Editing may permit a larger logo.

Use of a company logo is a time tested method for associating your merchant activities with reputation and trust.

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