I checked WinZIP too since it's installed at work, and you can't rename files from within that program either. 7zip might be a good suggestion for that purpose.
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But 7zip over WinRAR in general? I saw a test once between a bunch of compressors. 7zip actually didn't do that well. It generally compressed better than WinRAR for many file types, but only by a negligible margin. However on other file types, 7zip failed miserably compared to WinRAR. WinRAR never drops the ball like that. I'll see if I can dig it up.
Here is a test that compares overall compression to compression speed. You'll notice 7zip has a slight edge in overall compression, but is a fair bit slower.
http://www.rojakpot.com/showarticle.aspx?artno=4&pgno=11
Here is another page that shows something similar. 150 programs ranked by compression efficiency (ratio of total compression to total time to compress). WinRAR is ranked as high as number 3, 7zip first appears at number 17.
http://www.maximumcompression.com/data/summary_mf2.php
Here is a page that ranks the 150 compressors by total compression. WinRAR comes in 30th. 7zip comes in at 32.
http://www.maximumcompression.com/data/summary_mf.php
There is no reason to use 7zip over WinRAR. It's not as consistent. Its not as fast. It's not as efficient. It doesn't have half as many features.
Edit: Ah found it!
http://board.softpedia.com/index.php?showtopic=2079
Look at the Excel sheet in comparison.zip. 7zip does provide the best compression for most of the file types, but only by a small margin over WinRAR (BMP: 94.07% vs 93.01%; DOC: 89.38% vs 88.21%; GIF: 15.31% vs 13.54%). On the other hand, for some file types, 7zip falls far behind spectacularly (JPG: 58.85% vs 71.32%; MP3: 0.12% vs 0.43%; WAV: 7.99% vs 24.26%.
At most, 7zip beats WinRAR by a little over a percent, usually by much less. Yet there are a few file types that the 7zip algorithm almost completely fails on in comparison to other algorithms like RAR, and WAV is but one example.
It's just not worth the extra percent compression (in most cases, much less in others) when compression times are so much slower and you miss out on so many of the features of WinRAR.