Using お早うございます right next to a -です form

Question

If I have a sentence, for example

お早うございます 名前はエリアスです

Is having both ございます and です unnatural? because it feels weird. In which case should I use each of them in this example?

Answer 1

おはようございます is a set phrase, and for this reason it's usually written entirely in hiragana. It's a very common greeting that means "good morning" and, although it's polite, it is definitely an everyday word.

Since you can consider おはようございます a standalone word by itself, rather than the adjective 早い conjugated in the classical form ウ音便 (~おうございます), it's perfectly fine to use it alongside です (as Sundowner pointed out in his comment).

The entire sentence

おはようございます、名前[は]エリアスです

is in the polite style (丁寧語), which is the easiest of the three keigo styles (being the others the honorific 尊敬語 and the humble 謙譲語).

Moreover, and probably because 丁寧語 is the standard way of speaking politely in your everyday life, when talking about Keigo sometimes people only mean the honorific 尊敬語 or the humble 謙譲語 forms, because that forms are the ones that have different rules and different sets of vocabulary that are not used everyday and are harder to learn.

丁寧語 might be classified as Keigo, but you don't really need to learn specific ways to "use" it beyond using the ます conjugation instead of the plain form for verbs, adding です　after いadjectives and adding a few honorific prefixes ご or お here and there.

Answer 2

です is not needed next to おはようございます. When you say good morning to your friend or children, just おはよう without ございます is also OK. When you say to colleague in office, おはようございます is better to use. In kyoto, many of people say おはようさん to their friend. It's one of the dialect of Kyoto :-)