There are several ways, none of them as simple as they should be. This is what I consider the safest: (Note: This answer is long because it contains two sets of instructions: One for Word 2007 and one for previous versions.)
In Word versions prior to Word 2007:
First you'll create a new custom property with the value you want.
1. Click the File->Properties menu item.
2. Click the Custom tab.
3. In the Name text box, give your new property a name.
4. In the Value text box, give it a value.
5. Click OK.
Now you'll add fields that refer to that property.
1. Click where ever you want the property to appear.
2. Click the Insert->Field menu item.
3. In the Field Names list box, scroll down to the DocProperty field and select it.
4. In the Property list box, find your new property and select it.
5. Click OK.
Now, to make this more useful, save the file as a Word template:
1. Click the Save As menu item.
2. Select Document Template in the Save As Type list box.
3. Give your template a name.
4. Click OK.
The new template should now show up whenever you click File->New. Just change the property's value, select the entire document and press F9 to update the instances.
In Word 2007:
First, we'll create a Document Property for the customer's name.
1. Click the round Office button in the upper-left corner of the window.
2. Click Prepare, then Properties.
3. On the yellow bar, click Document Properties, then Advanced Properties.
4. Click the Custom tab in the Properties dialog box.
5. In the Name text box, give the property a name. Note that you can't use blanks or special characters.
6. Click in the Value text box and enter "Dummy Name". This won't be the actual name you use, but it will hold the place.
7. Click OK.
Now to create references to the new property. Click each place you want the customer's name to appear and do the following:
1. Click the Insert tab on the Ribbon.
2. In the Text group, click Quick Parts.
3. Select Field.
4. In the Field Name listbox, select DocProperty.
5. In the Property listbox that appears, select the field you just created.
6. Click OK.
This will put the current contents of the field there.
Now to save this as a template:
1. Click the round Office button in the upper-left corner of the window.
2. Click Save As and select Word Template.
3. Select Templates under Favorite Links in the left-hand window pane.
4. Give your template a name.
5. Click Save.
Here's how to use it. Every time you open a new document from the template, do this:
1. Click the round Office button in the upper-left corner of the window.
2. Click Prepare, then Properties.
3. On the yellow bar, click Document Properties, then Advanced Properties.
4. Click the Custom tab in the Properties dialog box.
5. In the Properties list box, find the property you created and select it.
6. It will pop into the Name text box and its value will pop into the Value text box. Change the Value.
7. Click OK.
8. Back in the text, press CTRL/A to select the entire document.
9. Press F9 to update all fields in the document. If you have other fields you want updated, you can postpone this for later.
Whoever uses the template should be aware that the fields can be overwritten, destroying their usefulness.
Hope that helps.