I wouldn't expect changing to a dedicated IP to result in any improvement in rankings. If anything, I'd expect a short-term drop, based on the experiences of some others when changing to a new IP address.

I hope in long term cause some effect. Any advantage you can think of?

it's been discussed here extensively:
site:webmasterworld.com dedicated ip rankings [google.com]

I think my first post wasn't clear. Forget about rankings.

Now that I have a dedicated IP must I configure something to take advantage of this feature, to improve site performance in any way? Is there something I can or must configure?

For the configuration, ask your hosting company, they will need to reconfigure your name-based virtual host to an IP-based one, as well as update your DNS to specify the new dedicated IP. It is not something you can do unless you manage the server and have full root access, which is not the case for shared hosting.

In your posts, you're not clear what you mean by "performance". If you mean in a technical sense, note that the actual IP address, whether shared or dedicated, has no effect on server performance - you site will be no faster or slower in either case.

If you mean performance in search or ranking, then a dedicated IP is not in itself a positive indicator, it merely may help avoid a negative indicator in comparison to an IP address shared with a banned or penalized site or sites. If you were not penalized before, then changing IP addresses will be of no benefit. If your "new" dedicated IP was previously used for a banned site, in fact it could make things worse. When using a dedicated IP address, you must also take care to avoid any duplicate-content issues caused by the server responding to direct requests for the IP address without specifying the host name.

This potentially negative indicator is, in any case, mostly hearsay and not based on much real hard evidence. Search engines simply don't filter by IP, especially for shared IPs from major hosting companies, other than for geo-location. The risk to the search engine of collateral damage is far too great.

If you are running a network of sites sharing one dedicated IP, a search engine may associate the sites, taking into account other factors such as content, interlinking and whois information. The absence of those other factors in the case of a shared IP from a shared-hosting company mean that search engines will be extremely unlikely to make any association between sites sharing the same IP address.

they will need to reconfigure your name-based virtual host to an IP-based one

They didn't tell me anything about that, and I don't really understand what they must do. What is my "name-based" virtual host?

Take care to avoid any duplicate-content issues caused by the server responding to direct requests for the IP address without specifying the host name

How can I tell if sever is responding to direct request for the IP address without specifying the host name. And what should I exactly ask the hosting to do?

you should make a http request to GET your ip address:
http://aa.bb.c.ddd/
and if that returns your home page with a 200 OK you have a domain canonicalization problem.
in any case the response should probably be a 301 Moved Permanently to your canonical home page url.
unless you have other plans for the url with your ip such as a control panel or site admin interface...

If your "new" dedicated IP was previously used for a banned site, in fact it could make things worse.

Do we have tool to check whether a particular IP had been banned before (as hosting companies are reluctant to disclose this).

search engine may associate the sites, taking into account other factors such as content, interlinking and whois information.

Does this mean that Google/Search engines will eventually come to know the relationship between two websites? If yes, then I think, going in for a dedicated IP is only to stay away from bad neighborhoods.