Add Column to assign Unique Name (Condition)

Hi Anonymous . I am able to achieve using below. #"Added Custom" is first capturing Name value for minimum branch, then replacing all values with it.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMjQwUNJRMgRix6RkpVgdmIgRRMQQKgRSYAzELqlpUBEjqKKIyiokEWMMEROIiDGSkClcKBYA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [#"Customer Code" = _t, Branch = _t, Name = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Customer Code", Int64.Type}, {"Branch", Int64.Type}, {"Name", type text}}),
    #"Grouped Rows" = Table.Group(#"Changed Type", {"Customer Code"}, {{"AllRows", each _, type table [Customer Code=number, Branch=number, Name=text]}, {"MinimumBranch", each List.Min([Branch]), type number}}),
    #"Added Custom" = Table.AddColumn(#"Grouped Rows", "Custom", each let minbranch = [MinimumBranch] in 
Table.ReplaceValue([AllRows],each [Name],Table.SelectRows([AllRows],each [Branch] = minbranch){0}[Name],Replacer.ReplaceText,{"Name"})),
    #"Removed Columns" = Table.RemoveColumns(#"Added Custom",{"AllRows", "MinimumBranch"}),
    #"Expanded Custom" = Table.ExpandTableColumn(#"Removed Columns", "Custom", {"Branch", "Name"}, {"Branch", "Name"})
in
    #"Expanded Custom"

Thanks
Ankit Jain
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Anonymous  Use below. Created a Duplicate Column(#"Duplicated Column") for this.

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMjQwUNJRMgRix6RkpVgdmIgRRMQQKgRSYAzELqlpUBEjqKKIyiokEWMMEROIiDGSkClcKBYA", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [#"Customer Code" = _t, Branch = _t, Name = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Customer Code", Int64.Type}, {"Branch", Int64.Type}, {"Name", type text}}),
    #"Duplicated Column" = Table.DuplicateColumn(#"Changed Type", "Name", "Common Name"),
    #"Grouped Rows" = Table.Group(#"Duplicated Column", {"Customer Code"}, {{"AllRows", each _, type table [Customer Code=number, Branch=number, Name=text,Common Name=text]}, {"MinimumBranch", each List.Min([Branch]), type number}}),
    #"Added Custom" = Table.AddColumn(#"Grouped Rows", "Custom", each let minbranch = [MinimumBranch] in 
Table.ReplaceValue([AllRows],each [Common Name],Table.SelectRows([AllRows],each [Branch] = minbranch){0}[Common Name],Replacer.ReplaceText,{"Common Name"})),
    #"Removed Columns" = Table.RemoveColumns(#"Added Custom",{"AllRows", "MinimumBranch"}),
    #"Expanded Custom" = Table.ExpandTableColumn(#"Removed Columns", "Custom", {"Branch", "Name", "Common Name"}, {"Branch", "Name", "Common Name"})
in
    #"Expanded Custom"