Can I print my public key using a custom logo? qrycode monkey allows me to print a qr code with my company's logo in the middle.

Q: Can I do the same for our public key?
You generally don't publish your public keys, you give clients an address (which is usually computed from a public key, but not exactly the same).

You can definitely put an address in a QRCode. Putting a logo in the QRCode doesn't change anything about that.

Generally you'd put a "bitcoin:" URI in the QRCode. More information can be found in BIP21.

Note that best practices involve not reusing addresses for more than one payment (and certainly not for more than one customer, or you wouldn't be able to tell what the payment was for), which may make it harder to use a custom web-based service for generating the QRCodes.