User Name is displaying incorrectly in SharePoint

Issue Description

A user's display name is incorrect on a SharePoint site .A user in your organization has recently updated some of his or her information (such as the user's display name) in Active Directory Domain Services. The information was updated correctly in the user Profile Service Application. However, on a specific Microsoft SharePoint 2010 Site Collection, that information was not updated.

Cause

The user is not synchronizing correctly to a Site Collection. This most likely occurs because the user is not flagged as Active on the Site. In Microsoft Office SharePoint 2007, you could remove the user from the All People group and re-add them. This option is no longer available in SharePoint 2010.

Resolution

In simple words – Note the permission of the user in the site. Remove the user from the site and add again. Detailed explanation is below

Important: If you remove the user from the All People group, all the user's permissions to this Site Collection are removed. Before you remove the user's permissions and re-add them, note the user's permissions. To do this, on the Site Actions menu, click Site Permissions, and then click Check Permissions.

The All People group is hidden in SharePoint 2010. However, to access this group, you can modify the following 

URL in the browser:

<Site URL>/_layouts/people.aspx?MembershipGroupId=0

For example, the URL will resemble the following:

https://contoso.com/sites/<SpecificSiteName>/_layouts/people.aspx?MembershipGroupId=0

If you remove the user from this group, this also removes the user from the userInfo table in the Microsoft SQL Server database. When you re-add the user, the user's information is updated in this table.

Reference