Import data between Google Sheets depending on whether specific data matches

I am including a quick screenshot that shows my question in a slightly more logical way, but basically I have two separate files, and would like to pull data from one into the other from specific locations, IF the names are matching from one cell to the other. Hopefully that makes sense:

Importing specific data between sheets if specific cell text matches

Update Here is the sheet where the data is being pulled FROM: https://docs.google.com/spreadsheets/d/1sfrmjqULdw4ELRIBmDURzlnIN0EzvpMCwHAmj8SuTMU/edit#gid=0

Here is the sheet where I would like to pull the data INTO: https://docs.google.com/spreadsheets/d/1HvPGl0ZjAO29DPTDkmpMVu9GFQIUJHqxOZF_itwt1to/edit#gid=1458193311

I should also note, that while I somewhat understand that I can ImportRange and specify some details, how do I specify a range related to a specific name, if that range is different for each name? I.E. Student 1 has data from A2:D10, but Student 2's data is F2:J10...etc.

Can we specify column and rows according to the position of a name?

Thanks @Ruben! I ended up using the following formula with a Named Range (StudentLookup), and then edited which column it pulls from, for each corresponding cell and it's data:

Cell B6: =INDEX(StudentLookup,MATCH($A6,other!$A$1:$A$9,0),MATCH($B$3,other!$A$1:$Z$1,0))

^for data I wanted in that cell and then for the next cell and so on:

Cell C6: =INDEX(StudentLookup,MATCH($A6,other!$A$1:$A$9,0),MATCH($B$3,other!$A$1:$Z$1,0)+1)

And I also just pulled the data directly from the other workbook into another sheet in this workbook for easier reference. Thanks again!