The change, introduced on 1 May, means google.ps now displays "Palestine" in Arabic and English under Google's logo.
Using the word Palestine is controversial for some. Israeli policy is that the borders of a Palestinian state are yet to be agreed.
In November, the UN gave Palestine the status of "non-member observer state".
The decision by the General Assembly was strongly opposed by Israel and the United States. Previously, Palestine only had "observer entity" status.
It followed an unsuccessful Palestinian bid to join the international body as a full member state in 2011 because of a lack of support in the UN Security Council.
Palestinians in general seek recognition for the state they are trying to establish and the adoption of the name Palestine.
Israel considers any formal use of the word Palestine as pre-judging the outcome of currently stalled peace talks. In much of Israel's official terminology the West Bank is referred to as Judea and Samaria.
In a statement given to the BBC on Friday, Google spokesman Nathan Tyler said: "We're changing the name 'Palestinian Territories' to 'Palestine' across our products. We consult a number of sources and authorities when naming countries.
"In this case, we are following the lead of the UN, Icann [the Internet Corporation for Assigned Names and Numbers], ISO [International Organisation for Standardisation] and other international organisations."
The Palestinian Authority (PA) welcomed Google's decision.
"This is a step in the right direction, a timely step and one that encourages others to join in and give the right definition and name for Palestine instead of Palestinian territories," Dr Sabri Saidam, advisor to Palestinian President Mahmoud Abbas, told the BBC.
"Most of the traffic that happens now happens in the virtual world and this means putting Palestine on the virtual map as well as on the geographic maps," he added.
Dr Saidam said that since the UN vote on 29 November, the PA had written to international companies, including Google, asking them to replace their usage of "Palestinian Territories" with "Palestine".

Allan Richards, 53, from Thaxted Road, Birmingham, served with the force for 31 years and is charged with committing the crimes against boys aged 11-18 between 1983 and 2013.
He also faces two counts of misconduct in public office.
West Midlands Police said it had referred the matter to the Independent Police Complaints Commission.
The former officer has been charged with a series of sexual assaults, indecent assaults and sexual touching.
The force said the charges of misconduct in public office related to alleged misuse of police powers to sexually exploit boys while he was a serving police officer.
Mr Richards was a police constable between 1980 and 2011.
He is due to appear at Birmingham Crown Court on Wednesday.

Food sales increased in February but overall Scottish sales declined year-on-year by 1.9%.
The Scottish Retail Consortium (SRC) said 2017 had "got off to a somewhat sluggish start" following a second successive month of falling sales.
It suggested consumers were responding to a combination of moderate wage growth and rising overall inflation.
SRC director David Lonsdale said: "In recent months we've seen a polarisation in the performance of food and non-food categories, which continued in February.
"Food sales continued to edge up, helped by good sales of wine and chocolates for St Valentine's Day as well as stronger demand for grocers' meal deals, which perhaps hints at less eating out during the period as consumers reined in spending.
"By contrast, non-food categories fell back once again, particularly clothing, footwear and household appliances, though there was continuing interest in mobile phones, wearable technology and a revival in gaming products."
He added: "These figures suggest Scottish consumers are maybe beginning to tighten their belts and acknowledge the strain from rising overall inflation and moderating wage growth, with council tax set to creep up soon too."
Internet giant Google has changed the tagline on the homepage of its Palestinian edition from "Palestinian Territories" to "Palestine".
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A former West Midlands Police officer has been charged with more than 30 child sex offences.
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Scottish retail sales fell last month as consumers started to "tighten their belts", according to new figures.