When I load Electrum my wallet name is the default name, something like "Wallet_Default". I've seen some wallets that have "test" profiles in them and they can really screw you over if you send your coins to it. I forgot what coin this was but I've heard nightmares about people losing withdrawals to it.
I have my private keys to the wallet. Is it safe to send BTC to it?
So what withdrawals are you talking about here? Is it from an exchange or a miners or some website that offers huge profit when you send them with x BTC? Or none on what I mentioned?
As long as you have the private keys of your wallet, then your coins are safe to send to anyone, the thing is we don't know if what/where do you want to send this coins as what you are asking.