Hi Ollie,
I assume from the description that you are using CRM On-Premise. I am also assuming that you access CRM using URL, which looks like http://<CRM_Server>:<Port>
This is the default setup for CRM without internet Facing Deployment. Under such scenarios, the CRM works on Single Sign-on and passes the Current Logged on Users credentials to CRM. This is the reason why you automatically log-in as the same user even after logging off and initiating the same session.
To Log-in as another user to CRM, you can follow either of the two options below:
Option 1:
1) Press and Hold the Shift Key down and Right Click on internet Explore.
2) Select Run as a Different User.
3) Give the credentials of the User you want to log-in to CRM as and click OK.
4) Navigate to CRM, this would give another Windows Security Log-in Prompt. Here also enter the credentials of the User you want to connect to CRM as.
Option 2:
1) Launch Internet Explorer.
2) Navigate to Settings -> Internet Options.
3) Select Security Tab.
4) Click on Local Intranet Zone and Sites.
5) Add the CRM web site to the Local intranet Zone.
6) Now, click on Custom level under "Security level for this Zone" and scroll to the bottom.
7) For the User Authentication Setting, select the Radio Button "Prompt for User Name and password" and save the changes.
The above changes (Option 2) will prevent the Single Sign-on for CRM and prompt the User for Credentials every time they try to access CRM from this particular computer.