Beginner question: primary and foreign keys

I would like to know if it’s a bad idea to not use the primary key from one table as the foreign key in another. What if I use a different field as the foreign key. Is it still a foreign key?

Maybe I can explain more… if I have a table called ‘projects’ with a field called ‘project_id’ (the primary key) and ‘name’… is it a bad idea to use ‘name’ as my foreign key in another table, i’m calling project_images. Project_images has a field called ‘item_id’ (the primary key) and ‘project_name’. I want to use ‘name’ from ‘projects’ and put it into ‘project_name’ in the ‘project_images’.

Thanks. Any advice would be really great. I can also post a link or take some screen shots to show what I mean.

I’m using:
MySQL client version: 5.0.22
Used PHP extensions: mysql