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