pivot_wider for Datasets

This is the simplest way I could think off:

ds = Dataset[{
  <|"Name" -> "Steven","Born" -> 1980, "Year" -> 2017, "Score" -> 115|>,
  <|"Name" -> "Steven", "Born" -> 1980, "Year" -> 2018, "Score" -> 230|>,
  <|"Name" -> "Joe", "Born" -> 1981, "Year" -> 2017, "Score" -> 70|>,
  <|"Name" -> "Joe", "Born" -> 1981, "Year" -> 2018, "Score" -> 300|>
}];
ds[
  GroupBy[#Name &],
  ResourceFunction["MergeByKey"][{{"Name", "Born"} -> First}]
][
  Values,
  Append[KeyDrop[#, {"Year", "Score"}],
    AssociationThread["Score_" <> ToString[#]& /@ #Year, #Score]
  ]&
]

If different people have different years, you might want to use KeyUnion to make the dataset square again. Documentation for MergeByKey is here

You can use the package "DataReshape.m" as shown below. (It is in my ToDo list to submit the corresponding functions to Wolfram Function Repository very soon.)

Load the package:

Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/DataReshape.m"]

Here is the original dataset:

dsData = Dataset[{<|"Name" -> "Steven", "Born" -> 1980, 
     "Year" -> 2017, "Score" -> 115|>, <|"Name" -> "Steven", 
     "Born" -> 1980, "Year" -> 2018, "Score" -> 230|>, <|
     "Name" -> "Joe", "Born" -> 1981, "Year" -> 2017, 
     "Score" -> 70|>, <|"Name" -> "Joe", "Born" -> 1981, 
     "Year" -> 2018, "Score" -> 300|>}];
dsData

Let us convert it to a “proper” long form with ID variables all except “Score”:

dsLong = ToLongForm[dsData, {"Name", "Born", "Year"}, Automatic]

Here we change the values of the column “Variable” to have the values of the column “Year” as suffixes:

dsLong2 = 
 dsLong[All, 
  Join[KeyTake[#, {"Name", "Born", "Value"}], <|
     "Variable" -> 
      StringRiffle[{#Variable, ToString[#Year]}, "_"]|>] &]

Here we convert to wide form with ID variables “Name” and “Born”:

ToWideForm[dsLong2, {"Name", "Born"}, "Variable", "Value"]

Both Sjoerd's and Anton's answers work nicely. Upon Sjoerd's solution using MergeByKey from the Wolfram Function Repository, I just wanted to post here for completeness that one can find almost the same solution with Merge from the Wolfram Language:

ds = Dataset[{
  <|"Name" -> "Steven", "Born" -> 1980, "Year" -> 2017, "Score" -> 115|>,
  <|"Name" -> "Steven", "Born" -> 1980, "Year" -> 2018, "Score" -> 230|>,
  <|"Name" -> "Joe",    "Born" -> 1981, "Year" -> 2017, "Score" -> 70 |>,
  <|"Name" -> "Joe",    "Born" -> 1981, "Year" -> 2018, "Score" -> 300|>
}];
ds[GroupBy["Name"], Merge[#, Identity] &][Values,
  Append[Map[First, KeyDrop[#, {"Year", "Score"}]], 
    AssociationThread["Score_" <> ToString[#] & /@ #Year, #Score]] &]