I can refer to Ms. X as a reference for ?

Can I put you down as a reference?

Eliane's suggestion doesn't make sense to me.

I therefore can name Mr. X as a reference for my knowledge of X?

Can you say it this way as a variation?

I therefore can put down Mr. X as a reference for my knowledge of X?

Can you say it this way as a variation?

You can also "use" someone as a reference.

Eliane, du solltest schon wenigstens einen Fragesatz formulieren, wenn das Satzzeichen am Ende des Satzes ein Fragezeichen ist. Desweiteren klingt in meinen Ohren dein zweiter Vorschlag, wie dein erster auch, verbesserungswürdig.

Der Vorschlag von *Alex* passt meines Erachtens.

Can I also "name" someone as a reference?

Aus diesem Grund kann ich X als Referenz für meine Kenntnisse in Y nennen.

Dies wäre der Satz in deutsch!

Ich bin weder englischer Muttersprachler noch eine Autorität, was die "Empfehlungssprache" betrifft, aber das wäre mein Vorschlag:

"Therefore I would like to refer you to X who is able to make a statement of recommendation about my knowledge of Y / in Y."

Danke. Gibt es noch Vorschläge von Muttersprachlern eventuell?

It all depends on context, e.g.:

"... and Mr Bloggs was my line manager there for 10 years. I am therefore pleased to put forward Mr Bloggs as a reference for my X skills / knowledge of X."

give someone as a reference

Usually in a letter, resume, you would simply say:
References:
Mr. X Ms. Y

You do not "name" someone as a reference.

I would say to STATE someone as a reference (in the resume or the usual reference list)

All are possible (AE). As with most phrasal verbs, 'put down' sounds less formal. I wouldn't use it in formal writing for a (potential) job or other position.

'Name' and 'list' sound best.

'State' sounds wrong to me. It doesn't come up in a google search, either. I know--that's not the only test, but nonetheless...