IBM eServer was a family of computer servers from IBM

IBM

International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

 Corporation.
Announced in the year 2000, it combined the various IBM server brands (AS/400, Netfinity, RS/6000, S/390) under one brand.
The various sub-brands were at the same time rebranded from:

• IBM AS/400 to IBM eServer iSeries, i for Integrated.
• IBM RS/6000 to IBM eServer pSeries, p for POWER
• IBM Netfinity to IBM eServer xSeries, x for eXtended architecture (with respect to "commodity" Intel-based servers)
• IBM S/390 to IBM eServer zSeries, z for Zero downtime

In 2005 announced a new brand, IBM System as an umbrella for all IBM server and storage brands.
The name change was finished in 2006 when the IBM xSeries became the IBM System x.

• IBM eServer iSeries became IBM System i
  IBM System i
  The IBM System i is IBM's previous generation of midrange computer systems for IBM i users, and was subsequently replaced by the IBM Power Systems in April 2008....
  
  
• IBM eServer pSeries became IBM System p
  IBM System p
  The System p, formerly known as RS/6000, was IBM's RISC/UNIX-based server and workstation product line.In April 2008, IBM announced a rebranding of the System p and its unification with the System i platform. The resulting product line is called IBM Power Systems.-History:It was originally a line...
  
  
• IBM eServer xSeries became IBM System x
  IBM System x
  The IBM System x computers form a sub-brand of International Business Machines System brand servers...
  
  
• IBM eServer zSeries became IBM System z
• IBM TotalStorage became IBM System Storage
  IBM System Storage
  IBM System Storage is the brand name for IBM's computer storage products, covering both Disk and Tape products.-DS3000 Series:The DS3000 products are made for IBM by LSI* DS3200...
  
  
• IBM eServer BladeCenter became IBM BladeCenter
  IBM BladeCenter
  The IBM BladeCenter is IBM's blade server architecture.-History:Originally introduced in 2002, based on engineering work started in 1999, the IBM BladeCenter was a relative late comer to the blade market. But, it differed from prior offerings in that it supported the full range of high powered x86...
  
  
• IBM eServer 1350 became IBM System Cluster 1350
  IBM System Cluster 1350
  The IBM Intelligent Cluster is a cluster solution for High-performance computing composed primarily of IBM System x, IBM BladeCenter and IBM System Storage components integrated with network switches from various vendors and optional high-performance InfiniBand interconnects...