Can you explain how it's not working for you? The Group By option will cause the Fit commands to perform one fit for each level of the grouping variable.
I used your data table and and ran Fit Y by X with myX and myY respectively.
2022-10-07_14-40-23.960.png
Then I chose the "Group By..." option from the Bivariate menu and used Name as the Grouping variable.
2022-10-07_14-41-15.973.png
2022-10-07_14-41-25.746.png
Then fit a line and got this result:
2022-10-07_14-41-44.993.png
2022-10-07_14-41-54.477.png
-Jeff