I'm not a male, but I'm gonna give my 2 cents anyway. I think most patients just want their nurse to be friendly, approachable, and professional regardless of gender. Sometimes, I think males are more reserved and don't give that first impression of friendly and approachable. Of course, that's a generalization.
I'm getting ready to start my first RN job, but I used to work as an intern on a busy med/surg floor and I'm not one of these overly friendly, "bubbley" types, but I'm not reserved either. I think there's a good happy-medium where you don't have to skip into the room and talk like a mouse, but you don't walk in all stoic either.
I would always walk in (as I knocked on the door) and say, "Hi, how are you doing? I'm "Suzy" and I'm a nurse intern so I'm gonna be helping the nurse take care of you until 7:00 tonight. Do you need anything right now or do you have any questions?" Sometimes they'd say no and sometimes they'd look around and it would be a drink or a blanket or something that they needed and I'd get it. Then, I'd get ready to go out and say, "If you need anything just use your call light and I'll be here" and then I'd make sure they actually HAD their light and knew how to use it. Of course I'd always use sanitizer going in and out too (that covered the first impression professional part).
It seems pretty basic and common sense-like, I know. BUT you'd be surprised at how many nurses I've seen walk into a room and not introduce themselves, not knock on the door, not make eye contact with the patients and their family, and not ask the patients if they needed anything. I've been a patient myself and didn't even know who my nurse was half the time. People would just walk in and out of the room, walk up to the computer, ask me some questions or look at my IV, and then leave. I don't know if they assume that patients know who they are because of their color coded scrubs (that patients don't usually even know about), or if they thought their name tags said it all (even when they're flipped over backwards).
I had sooo many patients and their family members tell me that I was their favorite. Most patients knew my name and weren't afraid to use it or send their family out searching for me either! It was crazy because in the grand scheme of things I really didn't do anything crucial when it came to their care. I had a patient one time whose nurse was a male and she asked me if he was a doctor. I told her, "No, John is your nurse." "John" should've already told her that. I think too many people forget the very basics.
So, I would say in making a good first impression, just go in and be friendly. Tell them plainly that you are their nurse. Ask them if they need anything, and let them know they can call on you. Being in the hospital can be scary and people want to know who they can call on if they need something or have a question. Having random people walk in and out and never come back after you ask for something just isn't the same as knowing a name and a familiar face - even if it is only for 12 hours.