What you're looking for is the host named site collection, which enables you to assign a unique DNS name to site collections. Or alternatively create an AAM for existing Site collection to achieve it. For example, you can address them as http://hr.mycompany.com or http://sales.mycompany.com.
The sample PowerShell code creates a new web application listing on port 80, and two host named site collections that use the Publishing Portal site template.
Create a web application to host your host-named site collections
$w = New-SPWebApplication -DatabaseName "WSS_Content" -ApplicationPool "SharePoint - Content App Pool" -Name "HostNameTest" -Port 80
Perform an IIS reset
IISRESET /noforce on each server before using the new web application
Create a root site collection
This is required for Search crawling content. For more information, see: http://technet.microsoft.com/en-us/library/cc424952.aspx#section2b
$webAppUrl = "web application url" #ex: http:// sharepointserver
New-SPSite $webAppUrl -OwnerAlias "SP\someusername" $w -Name "RootSC"
Create your site collections
$w = Get-SPWebApplication "HostNameTest"
New-SPSite http://hr.mycompany.com -OwnerAlias "SP\someusername" -HostHeaderWebApplication $w -Name "HostA" -Template "BLANKINTERNETCONTAINER#0"
New-SPSite http://sales.mycompany.com -OwnerAlias "SP\someusername" -HostHeaderWebApplication $w -Name "HostB" -Template "BLANKINTERNETCONTAINER#0"
So, you will have a web application with two two host-named site collections.
If SSL is a requirement, you can also create the web application and the host-named site collections using https (ex: port 443). But you will need to buy a wildcard certificate or a SAN certificate for *.mycompany.com. Also note that SSL is a requirement for certain features of SharePoint 2013.
To find more information:
You need to create a new web application and specify this as the URL, yes you could use an existing site collection an extend it using AAM but if you are starting from scratch a new web app and site collection is best.
Specify the host header what you want it to look like while creating new web application. or you can always use Alternate access mapping to look like http://hr.mycompany.com.