Learn Turkish: Bu isim çok kısa ama güzel. - This name is very short but beautiful.

In Turkish, there is no separate word for "is" in a simple present tense sentence like this. For the "it" form (referring to bu isim), the "is" is simply implied. So, Bu isim çok kısa literally reads as "This name very short", but translates completely as "This name is very short."

Does the word çok apply to both adjectives, meaning "very short but very beautiful"?

No, çok (very) only modifies the word immediately following it, which is kısa (short). If you wanted to say "very short but very beautiful", you would need to repeat the word: çok kısa ama çok güzel.

Can güzel be used to describe things other than physical beauty, like a name?

Absolutely! While güzel literally translates to "beautiful", it is an extremely common word used to mean "nice", "good", or "pleasant". You can have a güzel name, a güzel day, or even a güzel meal.

I know ama means "but". Does it connect full sentences or just words?

It can do both! Just like in English, ama can connect two full sentences, or it can simply connect two contrasting adjectives in the same sentence, as it does here with kısa (short) and güzel (beautiful).