We can add this for both the current version of one-offs and the new one.

We should check with UX whether we should add user-defined aliases to engine tooltips, and also whether typing user-defined aliases enters "search mode" for that engine.

We're going to show user-defined aliases in the tooltip and they will take priority over the default token aliases.

Backed out changeset 801076bd3a8a (bug 1647885) for browser_oneOffContextMenu_setDefault.js failures

Push with failures: https://treeherder.mozilla.org/#/jobs?repo=autoland&group_state=expanded&selectedTaskRun=SQP1ZFC-R1Cz1i56bGSJ5Q.0&searchStr=mochitest-browser-chrome&fromchange=fe71d126d639dbf96e6b5b87a3cc33c0fb9d0676&tochange=edabe12cf137f1dd876b4256716064bbcf7469b8

Backout link: https://hg.mozilla.org/integration/autoland/rev/edabe12cf137f1dd876b4256716064bbcf7469b8

Failure log: https://treeherder.mozilla.org/logviewer.html#/jobs?job_id=309889135&repo=autoland&lineNumber=3346

...
[task 2020-07-15T19:49:08.436Z] 19:49:08     INFO - Entering test bound test_urlBarEngineDefaultDisabled_normal
[task 2020-07-15T19:49:08.437Z] 19:49:08     INFO - Buffered messages logged at 19:49:08
[task 2020-07-15T19:49:08.437Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | One-off for test engine should exist - {"engine":{"_name":"Google","_isAppProvided":true,"_metaData":{"order":1,"alias":null}},"_inheritedElements":{".button-icon":{}},"initializedAttributeInheritance":true} != "undefined" - 
[task 2020-07-15T19:49:08.437Z] 19:49:08     INFO - Buffered messages finished
[task 2020-07-15T19:49:08.441Z] 19:49:08     INFO - TEST-UNEXPECTED-FAIL | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | One-off should have the tooltip set to the engine name - "Google (@google)" == "Google" - JS frame :: chrome://mochitests/content/browser/browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js :: openPopupAndGetEngineButton :: line 318
[task 2020-07-15T19:49:08.442Z] 19:49:08     INFO - Stack trace:
[task 2020-07-15T19:49:08.442Z] 19:49:08     INFO - chrome://mochitests/content/browser/browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js:openPopupAndGetEngineButton:318
[task 2020-07-15T19:49:08.443Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should have the correct id - "urlbar-engine-one-off-item-Google" == "urlbar-engine-one-off-item-Google" - 
[task 2020-07-15T19:49:08.443Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should now have the original engine's id for the button - "urlbar-engine-one-off-item-Google" == "urlbar-engine-one-off-item-Google" - 
[task 2020-07-15T19:49:08.444Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should have disabled the setting as default for the default engine - true == true - 
[task 2020-07-15T19:49:08.444Z] 19:49:08     INFO - Leaving test bound test_urlBarEngineDefaultDisabled_normal
[task 2020-07-15T19:49:08.444Z] 19:49:08     INFO - Entering test bound test_urlBarEngineDefaultDisabled_private
[task 2020-07-15T19:49:08.447Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | One-off for test engine should exist - {"engine":{"_name":"Foo","_shortName":"foo","_loadPath":"[other]/testEngine.xml","description":"Foo Search","__searchForm":"http://mochi.test:8888/browser/browser/components/search/test/browser/","_iconURL":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAQCAIAAACQkWg2AAABGklEQVQoz2NgGB6AnZ1dUlJSXl4eSDIyMhLW4Ovr%2B%2Fr168uXL69Zs4YoG%2BLi4i5dusTExMTGxsbNzd3f37937976%2BnpmZmagbHR09J49e5YvX66kpATVEBYW9ubNm2nTphkbG7e2tp44cQLIuHfvXm5urpaWFlDKysqqu7v73LlzECMYIiIiHj58mJCQoKKicvXq1bS0NKBgW1vbjh074uPjgeqAXE1NzSdPnvDz84M0AEUvXLgAsW379u1z5swBen3jxo2zZ892cHB4%2BvQp0KlAfwI1cHJyghQFBwfv2rULokFXV%2FfixYu7d%2B8GGqGgoMDKyrpu3br9%2B%2FcDuXl5eVA%2FAEWBfoWHAdAYoNuAYQ0XAeoUERFhGDYAAPoUaT2dfWJuAAAAAElFTkSuQmCC","_iconMapObj":"undefined","_metaData":{"loadPathHash":"RfTpH2lkFj90/1x8YKYIweUdv1GrWwdn5DWRzzXQujg=","order":7},"_urls":[{"params":[{"name":"test","value":"{searchTerms}"}],"rels":[],"resultDomain":"mochi.test","template":"http://mochi.test:8888/browser/browser/components/search/test/browser/?search"}],"_isAppProvided":false,"_orderHint":null,"_telemetryId":null,"queryCharset":"UTF-8"},"_inheritedElements":{".button-icon":{}},"initializedAttributeInheritance":true} != "undefined" - 
[task 2020-07-15T19:49:08.447Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | One-off should have the tooltip set to the engine name - "Foo" == "Foo" - 
[task 2020-07-15T19:49:08.447Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should have the correct id - "urlbar-engine-one-off-item-Foo" == "urlbar-engine-one-off-item-Foo" - 
[task 2020-07-15T19:49:08.509Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should now have the original engine's id for the button - "urlbar-engine-one-off-item-Foo" == "urlbar-engine-one-off-item-Foo" - 
[task 2020-07-15T19:49:08.509Z] 19:49:08     INFO - TEST-PASS | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | Should have disabled the setting as default for the default engine - true == true - 
[task 2020-07-15T19:49:08.513Z] 19:49:08     INFO - Leaving test bound test_urlBarEngineDefaultDisabled_private
[task 2020-07-15T19:49:08.529Z] 19:49:08     INFO - Search engine removed: testEngine.xml
[task 2020-07-15T19:49:08.590Z] 19:49:08     INFO - GECKO(3235) | MEMORY STAT | vsize 20975525MB | residentFast 1191MB
[task 2020-07-15T19:49:08.590Z] 19:49:08     INFO - TEST-OK | browser/components/search/test/browser/browser_oneOffContextMenu_setDefault.js | took 4784ms

https://hg.mozilla.org/mozilla-central/rev/6e4240fd5218

I verified this issue using 82.0a1 (2020-09-14) on macOS 10.13 and Windows 10 x64.
Adrian could you help me with Ubuntu verification?

Verified on Ubuntu 18.04 x64 as well, updating the flags accordingly to the above comment.

Hi,
I've been testing this and I've got a doubt. The default search engine all have an alias, but the added ones don't have an alias. This then produces that if I type @ on the urlbar, the newly added search engines don't appear listed. Is this ok?

Yes, that's expected. If you add an keyword to those engines that you added yourself (by double clicking in the pictured table) then they should show up when you type "@" and in the tooltip when you hover over their one-off.

(In reply to Florencia Di Ciocco from comment #10)

I've been testing this and I've got a doubt. The default search engine all have an alias, but the added ones don't have an alias. This then produces that if I type @ on the urlbar, the newly added search engines don't appear listed. Is this ok?

I spoke to UX about this and we decided we're doing to show all engines for searches for "@" regardless of whether they have a keyword assigned. I opened bug 1675052 for this.

Thanks for the reply :)