Vietnamese uses numbers for both months and weekdays
January: Tháng 1
February: Tháng 2
...
December: Tháng 12
For weekdays
Monday → Thứ hai (2nd day of week)
Tuesday → Thứ ba (3rd day of week)
Wednesday → Thứ tư (4th day of week)
Thursday → Thứ năm (5th day of week)
Friday → Thứ sáu (6th day of week)
Saturday → Thứ bảy (7th day of week)
Sunday → Chủ Nhật (Lord's day)
However, albeit the name, it should be noted that in Vietnam Monday is the start of week, and there is a song about that which everyone should learn from kindergarten, too.
It was said that this possibly originated from Portuguese when the Portuguese Jesuit missionaries came to Vietnam and created an alphabet based on Latin characters for Vietnamese.
Some other examples are the Mongolian, and Buryat languages, which use 2 systems for day of week names, one based on the planets and one based on ordinal numbers.
In Mongolia
Cyrillic Transliteration Rough meaning
Sunday бүтэн сайн өдөр büteŋ saiŋ ödör 'full good day' (='full holiday')
Monday нэгдэх өдөр neg dekh ödör 'first day'
Tuesday хоёрдахь өдөр khoyor dakh' ödör 'second day'
Wednesday гуравдахь өдөр gurav dakh' ödör 'third day'
Thursday дөрөвдэх өдөр döröv dekh ödör 'fourth day'
Friday тавдахь өдөр tav dakh' ödör 'fifth day'
Saturday хагас сайн өдөр khagas saiŋ ödör 'half good day' (='half holiday')
In inner Mongolia they use slightly modified names based on Chinese names
Cyrillic Transliteration Rough meaning
Sunday гарагийн өдөр garagiŋ ödör 'week day'
Monday гарагийн нэгдэх өдөр garagiŋ neg dekh ödör 'first day of the week'
Tuesday гарагийн хоёрдахь өдөр garagiŋ khoyor dakh' ödör 'second day of the week'
Wednesday гарагийн гуравдахь өдөр garagiŋ gurav dakh' ödör 'third day of the week'
Thursday гарагийн дөрөвдэх өдөр garagiŋ döröv dekh ödör 'fourth day of the week'
Friday гарагийн тавдахь өдөр garagiŋ tav dakh' ödör 'fifth day of the week'
Saturday гарагийн зургаадахь өдөр garagiŋ zurgaa dakh' ödör 'sixth day of the week'
In Buryat
Cyrillic Transliteration Rough meaning
Sunday гарагай нэгэн garagaj nägän 'one of the week'
Monday гарагай хоёр garagaj ȟojor 'two of the week'
Tuesday гарагай гурбан garagaj gurban 'three of the week'
Wednesday гарагай дүрбэн garagaj dürbän 'four of the week'
Thursday гарагай табан garagaj taban 'five of the week'
Friday гарагай зургаан garagaj zurgaan 'six of the week'
Saturday гарагай долоон garagaj doloon 'seven of the week'
Please find the traditional Mongolian texts as well as more information in the link since it's hard to paste the vertical texts here without breaking the layout
You can also read about the names of week in different languages here: Days of the Week in the West, Chinese, Japanese, Vietnamese, and Mongolian