Easiest way is conditional formatting.
Either icon on toolbar or Format, Conditional Formatting, Condition…
“Cell Value is”, “Equal to” and enter your name in a string, “mike”
Select new style and set up the format you want.
Set the range of cells you want to apply the condition to.
Edit in answer to comment.
A very messy alternate to conditional formatting is to use the STYLE function with a lookup table to find the style for each name.
However you need to then always copy the formula when you add the name to a different cell.
I think it might be better to use multiple conditional formats, unless you create a macro that runs on any cell change and uses a lookup table to select the format.
Edit to add sample Spreadsheet document with macro on event for cell content changed.