[Banter] So... I'm an English speaker, but most of my family are Welsh. (Dwi'n bwy mewn/ym Saesneg, ond ger Cymru. Arall, dwi'n gweithio mewn Cymru...(?).)
I shared a screenshot of this phrase to a family WhatsApp group, and asked my aunties if this was correct. I regret to inform you that my aunties are used to family members referring to them as "dragons"; and I have been promised several slaps (each), post-LockDown.
There was me thinking DuoLingo would improve my life chances... ;-) [/banter]
Helo is probably more common than Shwmae/S'mae. The latter is like a cross between "Hello" and "How are you?", a bit like UK English "Alright?".
I'd say Shwmae/S'mae can show a little more distance from the person you're speaking to than Helo, e.g. because you know someone less well, because you haven't seen someone for a long time etc. Helo is more neutral and can be used in all kinds of situations, distant or near. More familiar addresses would be things like Haia, Hei, Heia, which you can work out from English, and also Ti'n iawn?/Chi'n iawn? "You alright/OK?".
While, Most Names Do Have Versions In Other Languages, But That's Beside The Point. If You Were Introducing Yourself, You'd Likely Use Your Name As It Is In Your Native Language, However If You Were Using A Nickname, Say "My Friends Call Me Dragon", You'd Probably Want To Translate Said Nickname Into The Language You're Speaking, It'll Probably Feel More Natural, And It's Better In Case The Person You're Talking To Doesn't Know English, Although That Last One Seems Unlikely In Welsh.