Search for AD User by Partial Name

Get-ADUser -Filter {Name -like '*joe*'}
Details
This snippet will allow you to search for an Active Directory user with all of part of their name.

Example
PS C:\> Get-ADUser -Filter {Name -like '*joe*'}

DistinguishedName : CN=Joe Smith2,OU=CS,OU=Departments,DC=contoso,DC=com
Enabled           : True
GivenName         : Joe
Name              : Joe Smith2
ObjectClass       : user
ObjectGUID        : 8d0518b0-1ac8-43eb-9cbe-7632ab0756cb
SamAccountName    : JSmith2
SID               : S-1-5-21-3626140723-2009596974-1128677527-1330
Surname           : Smith
UserPrincipalName : [email protected]

DistinguishedName : CN=Joe Smith4,OU=CS,OU=Departments,DC=contoso,DC=com
Enabled           : True
GivenName         : Joe
Name              : Joe Smith4
ObjectClass       : user
ObjectGUID        : 1af50eb1-035f-4f8d-9867-2bb903457b90
SamAccountName    : JSmith4
SID               : S-1-5-21-3626140723-2009596974-1128677527-1333
Surname           : Smith
UserPrincipalName : [email protected]

DistinguishedName : CN=Joe Smith,OU=CS,OU=Departments,DC=contoso,DC=com
Enabled           : True
GivenName         :
Name              : Joe Smith
ObjectClass       : user
ObjectGUID        : 7f56f7b5-df52-473a-b50a-3d0dab42114b
SamAccountName    : JSmith
SID               : S-1-5-21-3626140723-2009596974-1128677527-1326
Surname           :
UserPrincipalName : [email protected]

DistinguishedName : CN=Joe Smith3,OU=CS,OU=Departments,DC=contoso,DC=com
Enabled           : True
GivenName         : Joe
Name              : Joe Smith3
ObjectClass       : user
ObjectGUID        : 7520a5f9-0129-4e58-ba7a-c933a44009fa
SamAccountName    : JSmith3
SID               : S-1-5-21-3626140723-2009596974-1128677527-1331
Surname           : Smith
UserPrincipalName : [email protected]

DistinguishedName : CN=Joel Henry,OU=Service Delivery,OU=Std Users,DC=contoso,DC=com
Enabled           : True
GivenName         : Joel
Name              : Joel Henry
ObjectClass       : user
ObjectGUID        : 18d6de0c-c48a-4f29-838d-f6bfa0e0d35b
SamAccountName    : JHenry
SID               : S-1-5-21-3626140723-2009596974-1128677527-3697
Surname           : Henry
UserPrincipalName : [email protected]

DistinguishedName : CN=Joe Stewart,OU=Marketing,OU=Std Users,DC=contoso,DC=com
Enabled           : True
GivenName         : Joe
Name              : Joe Stewart
ObjectClass       : user
ObjectGUID        : e06e9982-be9d-4372-9d0e-c6fceab557a1
SamAccountName    : JStewart
SID               : S-1-5-21-3626140723-2009596974-1128677527-3372
Surname           : Stewart
UserPrincipalName : [email protected]