Is there an alternative term for "boyfriend" when talking about an elderly man?

A possibility is "gentleman friend", which I have heard used in similar situations. It does not alway capture the distinction between "boy friend" and "boyfriend", but context can often clarify this. "Her gentleman friend" is more likely to correspond to boyfriend than "a gentleman friend".

For example

Is there a significant other in Aunt Wilma's life yet? Yes, she is going out to dinner with her gentleman friend tonight.

In most of the developed world, the traditional male-female courting towards and partnering of marriage has become cultural just one of many options. But in English at least the labels, nouns, verbs, or phrasing, really has not moved on much. Sure, people of all ages can have romantic relationships outside of marriage (and always have), but without the variety of nomenclature (at least in English) as for younger relationships. 'Boyfriend'/'girlfriend' just seem weird for people older than say ... 30? just because of the boy/girl part, even though the situation is mostly the same.

Companion, partner, friend all work fine, but they do have their primary, non-romantic meanings, and using them for romantic relationships, which people certainly do, always comes with some ambiguity nowadays: "Partner? Are they in business together? But they seem so close.". It always feels like there needs to be some disambiguation or a gesture or further explanation. Though these words have been used for romantic pairs, it is not (yet?) unambiguous even in context.

But as with all language, why is it necessary to force a single word onto things? That's what phrases are for. The seemingly empty but pragmatically accurate statement

"We're seeing each other"

gets the point across without that weird gossipy stigma about it.

TL DR:

• Yes 'boyfriend' sounds childish
• Companion, partner, friend are fine and can be disambiguated with further explanation.
• "We're seeing each other" is how I would say it to avoid all the issues.

No, not really. There is a quote I've heard several times but can't quite put my finger on that addresses this, that criticizes English and its puritanical history as leaving it sorely lacking in adequate terminology for such things, thus forcing English speakers to use infantilizing misnomers like "boyfriend" and "girlfriend," along with odd euphemisms, and that's if there's a term at all, which there often isn't, like is actually the case here.

I mean, you could use a term like "gentleman caller," but only if you don't mind sounding like you're a character in Jane Austen novel and only if you don't mind that, while it does get rid of the infantilizing "boy" misnomer, it falls short of denoting the man is elderly, never mind how it may be a misnomer if the man isn't actually, by definition, a "gentleman." Like I said, English, because of the English's storied historical weirdness about sex and relationships, is sorely lacking in adequate terminology for such things, a veritable famine.

Is there a reason one couldn’t use “beau” in this context ?
While it may be somewhat dated, that could be construed as making it more appropriate here.