Well, I don't know in Spain but in Latin America we say
Feliz cumpleaños = Happy birthday
Feliz cumpleaños [nombre] = Happy birthday [name]
Feliz cumpleaños [nombre de cariño] = Happy birthday [special name] (For close friends)
To all these expressions you can add many phrases where you express your enthusiasm or your care
Feliz cumpleaños, muchas felicidades
Feliz cumpleaños, que lo pases [muy feliz / muy bien / excelente]
Feliz cumpleaños, muchas felicidades, que lo pases [muy feliz / muy
bien / excelente]
¡Feliz cumpleaños y que cumplas muchos más!*
¡Feliz cumpleaños, muchas felicidades y [muchos] éxitos!
Usually we start with feliz cumpleaños and then we add something else. Sometimes it depends on the relationship with the other person and that could be followed with a half hug or a full hug or just a handshake
At work, strictly in Latin America some people develop a strong relationship with their bosses, so they can give a half hug, it means you approach to the other and your left hand on the back of the other person and your right hand on his right arm (I'm just trying to give an example not a rule). Women in Latin America are more emotional and they can give a full hug with their female bosses or co-workers but with males are more formal. Only if that girl is your partner in crime, she will give you a full hug.
Remember it depends on how close is your relationship with the other person.
In North America, at work, they tend to say happy birthday face to face without contact (mostly but not a rule) and that's it. They follow their lives.