「both」の日本語は何ですか？
例えば:

"Good luck to both of you!"
"I wish the best for both of you!"
"Thank you, both!"

ありがとうございます。Oh, also for expressions such as "I like both cats and dogs"

Question

「both」の日本語は何ですか？
例えば:

"Good luck to both of you!"
"I wish the best for both of you!"
"Thank you, both!"

ありがとうございます。Oh, also for expressions such as "I like both cats and dogs"

Answer

As Misaki has already said, 2人とも/どちらとも、どちらも and additionally 両方とも are major translations for "both".

"Good luck to both of you!" -> 2人とも頑張ってね！
"I wish the best for both of you!" ->2人ともに成功を祈ってるよ！
"Thank you, both!" -> 2人ともありがとう！
"I like both cats and dogs" -> 猫も犬もどちらも好きです/猫も犬も両方好きです

so like, you can use どちらも and 両方 interchangeably when you mention about things.

Answer

I think, 二人とも is used for people and どちらとも/どちらも is used for things. "I like both cats and dogs" = 猫と犬どちらも好きです。Waiting for a native speaker to correct me.