I know it's a stretch, and I'm pretty sure it's not, but is 名前 related to name? I always thought it was weird that they were so similar in pronunciation.
It's just a coincidence and an example of a false cognate.
The etymology is covered here in Japanese.
Basically, the term "名" has been around for a pretty long time with the same meaning as 名前. It's thought that the 前 part is an honorific that was added some time later. Early uses of the full word 名前 can be seen in use in relatively modern times. The English term for it seems to be "modern" in the historical sense, but in Japanese 近世 seems to refer roughly to the Azuchi-momoyama period through Edo, roughly 1500s to mid 1800s. Not quite sure exactly when the first recorded use was. It was widely used from the Meiji period onward.
I'd like to add onto ssb's answer, further exploring the etymologies for these terms.
I use Shogakukan's 国語大辞典【こくごだいじてん】 (KDJ) as one of my main sources. This dictionary includes more etymology (word-origin) information than most Japanese dictionaries that I've seen.
Here's the KDJ entry for 名前. As we can see, the earliest citation is from 1720, with a sense closer to "appellation, what something is called, the label put ʻin front of’ something". This is slightly different from "name" per se. The actual "name" sense, in terms of "a person's or thing's proper name", appears from 1731.
Both of these citations are early enough that influence from English is exceedingly unlikely -- the English language had little relevance for Japanese until the Perry Expedition of 1853.
That said, Dutch did have some influence on Japanese much earlier, from around 1600, and the Spanish and Portuguese even earlier, from 1542. So it still bears asking if a European language may underlie the Japanese term 名前【なまえ】.
Derivation of 名前【なまえ】
This is clearly a compound, of 名【な】 "name" + 前【まえ】 "front". The "name front" translation sounds super weird in English, but we must remember that word order is different in Japanese. It's worth noticing too that there are other Japanese compounds that end in 前【まえ】 in reference to something ʻput in front’, such as 建前【たてまえ】, or 一人前【いちにんまえ】, etc.
The straightforward compound nature, plus the late appearance of this term in the historical record, presents a strong case against this being at all related directly to any European word.
But what about 名【な】? Might that be at all related?
Here's the KDJ entry for 名. We see that the first citation is in the Man'yōshū, a large poetry collection finalized around 759 CE, and the first large corpus (collection of texts) with Japanese written phonetically and grammatically as Japanese. Other ancient texts like the Kojiki of 712 or the Nihon Shoki of 720 are mostly written in a kind of Classical Chinese, and thus don't provide us with much information about the ancient Japanese language.
So we know that the word 名【な】 with a sense of "name for a person or thing" has been around unchanged for a very long time.
Derivation of 名【な】
This same sense of "name", and mostly the same pronunciation -- albeit with a longer vowel value, as //naː// -- is reflected as well in the various Ryūkyūan languages, strongly suggesting that this is a cognate term inherited from the Proto-Japonic stage of the language family. See also the Wiktionary entry for 名, which includes a few of the Ryūkyūan terms.
The English term clearly has a final consonant, and nothing to do with "front". Where did this come from?
Derivation of "name"
As visible in various dictionaries, the English term traces back to Old English, back to Proto-Germanic, ultimately back to the reconstructed Proto-Indo-European (PIE) term h₁nómn̥. See, for instance, the Merriam Webster entry, or the Wiktionary entry.
So while English is an unlikely source for Japanese namae, or Japanese na, what about PIE?
Likelihood of relatedness to English "name"?
The Japonic term is consistently realized as na, a single syllable with no final consonant.
The PIE reconstruction, and pretty much all the cognates in descendant languages, include a closing nasal consonant //m// as either the final sound in the word, or the close on the first syllable.
Given the known and reconstructed phonetic rules for Japonic languages, I'm not aware of any means by which a (mostly polysyllabic) word with a core syllable ending in //m// would shift to a monosyllable with an open vowel and no final consonant.
Conclusion: Highly likely to be wholly unrelated.
It's actually surprisingly easy to find words in any two languages that kinda sorta sound similar and kinda sorta have similar meanings. If you're interested in word origins and comparative linguistics, I highly recommend you read "How likely are chance resemblances between languages?" The author even lays out a well-backed-up mathematical model for determining the likelihood of such non-cognate similarities.
A different poster brought up the possibility that Japanese 青空【あおぞら】 is somehow related to English azureus.
青空【あおぞら】 is clearly a compound, consisting of 青【あお】 "blue" + 空【そら】 "sky".
Meanwhile, azureus is Latin, not English, and traces in turn to Arabic, and then to Persian. See the Wiktionary entry for azureus.
The Persian term لاجورد (lâjvard, “lapis lazuli”) is itself probably also a compound, consisting of lâj "blue" + vard "stone".
- Japanese ao and Persian lâj both mean "blue", but the phonetics certainly don't match up very well.
- Japanese sora means "sky", while Persian vard means "stone" -- these don't match in either meaning or sound.
If you think you've found a cognate, dig. Chances are quite high that the ancestor terms of the modern "matches" you've found are not actually matches at all. "What if" can be a fun game, but it won't get you very far.
Since 名 alone means name, there is no need 前 to be added to form a word to mean "name". This is true to other countries such as Korea which also uses Chinese characters.
And 前 means front(or first in certain context),
so 名前 together could literally interpreted as "first name".
this makes me doubt/wonder if the usage of 名前 instead of 名 as a Japanese term for "name" indeed has something to do with Japanese people's first encounter with English speaking foreigners hundreds of years ago.
It might be a true cognate.
I see responses above that say they aren't close in pronunciation, but the roots are close. In Old English name was "nama" and linked with similar sounding words in other languages. 「なまえ」is a similar pronunciation. https://www.etymonline.com/word/name
I've definitely seen other similar cognates while learning Japanese that appear coincidental and potentially connect to ancient roots, even though the etymologies tend to document the Chinese character development, rather than linking to other potential influences.