All three of these examples can be used, but the most popular is "interior design". You can always comment about the interior by saying, "I like your interior design."
これらの例のいずれも使うことが出来ますが、最も一般的なのは"interior design"です。
内装については次のようにコメントできます：
"I like your interior design."（内装がいいですね）
Interior design is the art or act of decorating the inside of a room or entire building to look pleasing to the eye. Interior design is the art of working with colors and optimizing the space of an area to make it practical for daily use. An interior designer is the title of the person who actually decorates the interior space.
Decor' is used to refer to the interior design of a room or building. 'Decor' can also be found as a part of the word 'decoration' which refers to specific objects that adorn a space or object -- e.g.: 'The glass bulbs are used for decoration on Christmas trees.'
Decor'は部屋や建物のインテリアデザインを指します。
'Decoration'という言葉の一部としても'Decor'が使われています。'Decoration'は場所や物を飾る特定の物を指します。
例：
'The glass bulbs are used for decoration on Christmas trees.'
（ガラス球はクリスマスツリーのデコレーションに使われます）
"Interior design" is more formal and more likely to be used by a professional. Most native speakers might use the word "furnishings" which can describe all the decorations and accessories inside of a room or building.
"Decor" is also a popular word used, this is short for decoration.
When you are talking about the style/decoration in a room this is referred to as 'interior design' you can also call this 'decor' which means the things/decorating that is in the room
furnishings are what we call furniture in the room
"Interior design" is a term used to describe the decoration of the inside of a house or room. "Interior design" is a way to express your own personal style when decoration your house or arranging furniture within your house. You can employ some businesses to decorate the inside of your house for you and we call these "Interior designers".
"Interior designer"
Is the term used to describe someone who works in this particular field, of designing the interiors of a home or buildings.
"Interior design" is the act of designing someones house or building.
"My friend's occupation is an Interior designer"
"Interior designer"（インテリアデザイナー）は、家または建物の内装を設計する仕事をする人をいいます。
"Interior design"（インテリアデザイン）は、家または建物の内装を設計することをいいます。
"My friend's occupation is an Interior designer"
（私の友達はインテリアデザイナーをしています）
日本 
カナダ 
アメリカ合衆国 
イギリス 
