Question about recurring text in database field

[Macamba .]

I designed a database application in Java which I use to keep track of time I spend on different tasks. The user (atm only me) can enter definitions of projects and activities to choose from when keeping time. The definition of a project activity is done in the table 'projectdef', time spend is stored in the table 'projects'.

For instance, I have a table 'projectdef' with the following activity definition:
Field - Content
proid - 7
cust_name - ACME Inc.
projectnumber - p10001
project - TimeKeeper
activity - DAOTest
tarif - 65
perident - greaper
active - 1

I can select this record and use it to add a new row in my 'projects' table. What I do not like in the current approach that I will keep seeing cust_name and project repeated. Is that a wast of storage space, or does MySQL use a nifty solution behind the screens for this?