you can do it with
1) VLOOKUP()
2) INDEX() MATCH()

type the below formula in sheet2 cell B2
(suppose in Sheet1, names are mentioned in column A and phone numbers are mentioned in column B)

=IFERROR(VLOOKUP(A2,Sheet1!A:B,2,false),"")

here ...
A2 = is the name on Sheet2, whom phone number u want to search
A:B = is a range on Sheet1, where your data exists
2 = is used to get data from 2nd column of range
False = in your case, it will be.