Your code should work fine, my tests did. But try this instead and see if it works for you.
$GroupNameLike = Read-Host "Enter group name"
Get-AdGroup -filter "name -like '$GroupNameLike'" | select -expandproperty name
If you’re wanting to allow incomplete group names to be entered, you may want to add asterisks like this.
$GroupNameLike = Read-Host "Enter group name"
Get-AdGroup -filter "name -like '*$GroupNameLike*'" | select -expandproperty name
If you’re wanting the value of name, leave it as just Select -ExpandProperty name. If you want an object with a name property, change it to Select Name