The exact cell formula depends on how your lists are arranged. For example, are they on different worksheets? In different workbooks? Different files? How often is either list likely to change? Will the alphabetical ordering of customer names ever be problematic - for example, will Mc come after all the Ma's, or will it be in with the Mac's?
Assuming the list will change sometimes (old customers drop out, new ones sign up), and might sometimes be out of alphabetical order, the Vlookup() function in Cell B1 is probably your best bet. Within the brackets you will need to enter the arguments which will, in effect, tell B1 to "check the customer number immediately to the left of this cell, then locate the same number in the customer list, and whatever customer name is alongside it, display it here".
Once you get the arguments right, Vlookup will provide you with a formula which you only need to enter once (in Cell B1). Then just fill the same formula down the column as far as you need. Although I haven't used it for a while, I recall that there is an additional argument you need to include to warn Vlookup() that the list might be out of order sometimes, otherwise it may return wrong info. This is important because your spreadsheet software may disagree with you as to what constitutes correct alpha order. However, if your customer numbers are always in their correct order, the issue may not arise.
There are variations on the theme - for example, Hlookup() - but Vlookup is most likely the one you want. If you are using Excel, the help line will give you all the info you need.
