How do I know if I'll have an issue with trademarking for my brand name selection?

Do you know if calling hair care brand 'Glamr' is going to be an issue to copyright if there are brands like Glam Glow and a magazine called Glamour magazine ? We will be selling our own branded products. These are the two I am somewhat worried about. Glam Glow sells face masks, moisturizers, serums and toners. Glamour magazine is a womens lifestyle magazine that talks about makeup, fashion, hair, entertainment and beauty in general. I don't want to start the process yet as it is too expensive at this point in time. Considering I have worked with you a few times now, what do you think the likelihood is of getting "Glamr" through. I have done a trademark search for Australia and also the USA What would be the best option or easiest option? To simply come up with a new brand name or add a second work to the end of Glamr. Such as Glamr and Shine or Glamr Hair