Another word of caution to be mindful of.
Square are based in California and therefore subject to the FOSTA and SESTA legislation in the US. They will be careful not to get caught facilitating any sort of sex work, and will have thresholds and other flags that trigger a closer look at your transactions. Deposits might not raise any eyebrows but big $$ might. Having money seized has been a problem for people using PayPal deposits etc... and Square will be aware of their issues.
If there is a similar payments system operating in Europe or Australia it would be much safer.
Lady Companion, are you using the account of another business altogether? That would be a perfect way to go if transactions are just mixed in with someone who already has the merchant account set up.