Why new public key for every new request? I created Bitcoin accounts using different clients but all clients I tried prompt for new public key for each request. My question is shouldn't be the public key one's identity which one should be able to publish and own even changing bitcoin clients.

Clients always give me new key which makes me feel insecure to use a single key for overtime use. For example I created and want to stick to this key: 1N3eYqC7EJdbBBXQ6ntQpmzedVrGeG8iqJ but if I go create another request new key will be generated, the main concern is should I be sure that this key will always be pointed to my wallet? As I am not sure and don't have bitcoins to test if coins are received at this address.

I have used multiBit and Android App, none of these give private key as far I browsed. I am looking for an 'identity' to publish for receiving any number of payment, like we can share our paypal email to receive payments.
The reason is privacy.

If you reuse the same key for every transaction, everyone who ever transacts with you can infer your entire balance.

No, public keys should not be identities, exactly because the transactions to them are public too. Your ability to create many pseudonyms in the system the only way through which it has any privacy. By reusing addresses you hurt your privacy, but also that of others who interact with you.