Compare two names list and compare other column aftrerwards

Okay, try this in Sheet1!C3:

Formula:

=IFERROR(INDEX(Sheet2!$A$2:$A$20,MATCH(A3&B3,Sheet2!$B$2:$B$20&Sheet2!$C$2:$C$20,0)),"")

Confirm with Ctrl+Shift+Enter (this is an array formula, so just using enter will NOT work), if it is entered right curl braces will be at the start ({) and end (}) of the formula
Drag this down to C19
This will give the Value of Sheet2 Column A if there is a match

Next, select the range of A3:C19 on sheet1,
go to Conditional Formatting, New Rule, Use Formula

Formula:

=$C3<>""

Format,Fill, select a fill color for a match, OK,OK

go to Conditional Formatting, New Rule, Use Formula

Formula:

=$C3=""

Format,Fill, select a fill color for a non-match, OK,OK

Note - the name matches must be exact, if there are leading or trailin spaces in one name that is not in the "matching name", the result will be negative on the match

See Attached

Hope this helps