No you can't change the name. So yeah that's a drawback compared to Masuda method. However, you have a better chance of getting a flawless shiny using TSV. Each method has advantages and disadavantages what it really boils down to though is how much time your willing to invest. If you have hours to invest then maybe Masuda method would be a decent choice. It's your call.
Something else:
Mew
Impish
31
29
31
X
31
31
Keep or toss (I might actually consider tossing but want thoughts) also does impish mew need that flawless attack?
I would toss but it's not the worst keep.