Yes, when you deploy via change sets, you have to include all the individual pieces of an object explicitly. Fields and layouts are the ones that catch me most often. It can be a major nuisance to wade through the fields to find the right ones if you have many objects and fields in your data model. Sorting by Type (object name) can help, but there may still be a lot of clicking on "next".
In the comments, SFDCfox points out the Change Set Components section of the Change Set page has a "View/Add Dependencies" button. This will show you a list of items (fields, buttons, list views etc.) that are connected with the object or objects already in your change set. This list will be shorter than the list of all fields. However, bear in mind that:
If your change set contains more than 2500 dependencies you will only
be able to see the first 2500 in the view dependencies page.
If you deploy objects with Eclipse, you won't have this problem with needing to list individual fields etc. Of course, getting up to speed on Eclipse is not a small task.