How do I update column values to equal column values based on another column?

I have a sql table like this,

+-------+-------+-----+
| name  | start | end |
+-------+-------+-----+
| Joe   |    14 |   - |
| Joe   |    13 |   - |
| Steve |    11 |   - |
| Steve |    15 |   - |
| Bruce |    10 |   - |
+-------+-------+-----+

and i want to update the values for column “end” with the values from “start” for each unique column value “name”, so it looks like this.

+-------+-------+-----+
| name  | start | end |
+-------+-------+-----+
| Joe   |    14 |  14 |
| Joe   |    13 |  13 |
| Steve |    11 |  11 |
| Steve |    15 |  15 |
| Bruce |    10 |  10 |
+-------+-------+-----+

my question is: how do i do this in SQL code, and how would it look like with a PHP mysql query?