that is what insert on duplicate key update is for.
The Manual page for it is here.
The trick is that the table needs to have a unique key (can be a composite) so that the clash of doing an insert can be detected. As such, the update to occur on that row, otherwise an insert. It can be a primary key, of course.
In your case, you could have a composite key such as
unique key(theName,theDate)
If the row is already there, the clash is detected, and the update happens.
Here is a complete example
create table myThing
(   id int auto_increment primary key,
    name int not null,
    values1 int not null,
    values2 int not null,
    dates date not null,
    unique key(name,dates) -- <---- this line here is darn important
);
insert myThing(name,values1,values2,dates) values (777,1,1,'2015-07-11') on duplicate key update values2=values2+1;
insert myThing(name,values1,values2,dates) values (778,1,1,'2015-07-11') on duplicate key update values2=values2+1;
-- do the 1st one a few more times:
insert myThing(name,values1,values2,dates) values (777,1,1,'2015-07-11') on duplicate key update values2=values2+1;
insert myThing(name,values1,values2,dates) values (777,1,1,'2015-07-11') on duplicate key update values2=values2+1;
insert myThing(name,values1,values2,dates) values (777,1,1,'2015-07-11') on duplicate key update values2=values2+1;
show results
select * from myThing;
+----+------+---------+---------+------------+
| id | name | values1 | values2 | dates      |
+----+------+---------+---------+------------+
|  1 |  777 |       1 |       4 | 2015-07-11 |
|  2 |  778 |       1 |       1 | 2015-07-11 |
+----+------+---------+---------+------------+
As expected, insert on duplicate key update works, just 2 rows.