Unfortunately, you need to advertise your company name or yourself. Because Cure is a Client Partner of Submit Candidate Technologies and you have a contractual agreement with Submit Candidate as a recruiting vendor not Cure.
You also do not want to limit yourself to just being known for Cure job openings. We will be adding additional Agency Partners with other open job opportunities soon and you will want to recruit for them as well. We know this might be different than what you were expecting, but our top recruiters are good because they have a good name, they build their brand and their business name.
This is about you now establishing your name, your brand and being known as a trusted adviser to your candidates. Build your book of candidates. You'll want to promote various open jobs from different agencies, so don't limit yourself.
Think of the candidates as professional sports players and you are their Agent. Your job is to represent them and get them the best opportunity. You want them to trust you and want to work with you.
Lastly, please do not promote the hospital name. We are not allowed to contractually and more importantly, the candidates will go around you. The hospital name is your secret card. Post everything else.