The best replacement for logon is login.

The best alternatives to logon are rated as following:
★★★★★  login
★★★  log on
★  account logon
  last logon timestamp
  everyone
  domain logon
  log-on
  lastlogontimestamp
  logon

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Speaking about logon, one probably shouldn't forget about ctrl alt del.

Other search terms related to logon and their ratings are:
★★★★★ ctrl alt del
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Google Trends

Scale is based on the average worldwide traffic of logon in all years. Click on graph for more.
logon
login
log on