This should be a blue card, a rare card and worded in such a way that it properly defines when the copy effect starts and when the copied creature is chosen.
The ability granted as a static ability. Static abilities cannot target though. You choose targets for activated abilities and triggered abilities (and spell abilities, but you don't grant the with Equipment to the equipped creature anyway).
I suggest rather than using a static ability, you use "When ~ becomes attached to a creature, that creature becomes a copy of target another creature for as long as ~ remains attached to it."
You could also use "another creature of your choice" rather than "another target creature" in which case you could also use "As ~ becomes attached" rather than "When ~ becomes attached".
If you are settled on green, you should have this copy a creature "you control", but switching to blue seems a better fit with the flavor connotations that come with the card name Trench Coat.
That name... It speaks to me.
This should be a blue card, a rare card and worded in such a way that it properly defines when the copy effect starts and when the copied creature is chosen.
The ability granted as a static ability. Static abilities cannot target though. You choose targets for activated abilities and triggered abilities (and spell abilities, but you don't grant the with Equipment to the equipped creature anyway).
I suggest rather than using a static ability, you use "When ~ becomes attached to a creature, that creature becomes a copy of target another creature for as long as ~ remains attached to it."
You could also use "another creature of your choice" rather than "another target creature" in which case you could also use "As ~ becomes attached" rather than "When ~ becomes attached".
If you are settled on green, you should have this copy a creature "you control", but switching to blue seems a better fit with the flavor connotations that come with the card name Trench Coat.
You want to remove "converted" from that last ability. The conversion is from "cost" to "number". A flashback cost needs to be a cost, not a number.
No Mutant on the type line, I notice.