I never used this kind of operations with Skrill but I did with PayPal and I assume It's the same thing. If you withdraw from the account to the card then It should something like "Skrill - your name here -" should appear so yeah that fake name will probably be visible.
Do you think the bank could get suspected about me receiving those transactions.
This is not a wire which is sent in my name still the bank can see those notes baring a random name.