저는 "라리사"라는 이름도 굉장히 좋은 것 같습니다. 한국인의 이름은 대체적으로 3음절로 이루어진 경우가 많아요. 또 리사라는 이름의 발음도 굉장히 좋구요. 

(I think "라리사" itself is great for korean name. Many korean names are 3 syllables. Also "risa" is easy to pronounce in korean. )

성을 '라' 이름을 '리사'라고 한다고 생각하면 어떤가요?

(How about thinking '라' for familly name and '리사' for first name?)

많은 한국인들처럼 한자로 뜻을 붙인다면,

(If i make your name using hanja like many koreans,)

영리할 리(悧), 생각 사(思) 를 사용해서 영리하고 사려깊다는 뜻을 가진 이름이 될 수도 있겠네요.

(悧-sounding 'li/ri, meaning 'smart, clever'-and 思-sounding 'sa', meaning 'thought, thoughtful'- would be nice.)

I think it is not bad to use the name. You don't need to have a Korean name. Like many Korean who speak English don't have English name and they use his Korean name. I think your name is not bad in Korea. I recommend you to use your name as is.

Many Korean like to make friends with foreign people, and they want to know your (original) name. That's why you don't have to have  Korean name.

갈매기의 뜻을 갖는 것으로 생각해 봤습니다.

구호(鷗湖):

구(갈매기), 호(lakes).

It sounds a bit manely to Koreans phonologically.

구슬(鷗璱):

구(갈매기), 슬(푸른 구슬; a ball-shaped blue gem/bead; a jade marble).

The final liquid consonant causes soft and far-reaching resonance.

It sounds feminine, ladish, and womanly.