You might be better served creating a table of names and emails where the name you want to lookup is column a then any other information you want would start in b. Excel has a limit as to the number of nested if statements, not to mention the headache of trying to change it later and tracking all the parenthesis, one miss-type and you could spend hours figuring out where you forgot a parenthesis.
If you don't want to/can't use a vlookup, the switch expression might be better.
The Syntax of the SWITCH function includes 4 parameters. Out of 4 parameters of SWITCH functions, 3 are mandatory, and the fourth one is optional based on our requirement.
Expression: This is simply the value or cell we are trying to test the logic.
Value1: This the test value or logical value comparing to the Expression. We can give 126 logical tests.
Result1: If the first logical test is true, what should be the result we want.
Default or Value 2: Here, we can see two things. One is Default; if the first logical test is FALSE, what is the default value we want. The second one is Value2; this is the second logical test for the Expression.
Result 2: This is the result of the second logical test we are testing.
As for your IF statement you need to wrap the evaluated value in quotes since it's text.
=IF(F4="Anna",“anna@gmail.com”,IF(F4="Julie", “julie@gmail.com” ,IF(F4="Diana",”diana@gmail.com”)))