Having just discussed this topic with a user, I can provide a bit of information.
The pdf based on the Oxford style guide says this:
Style guide pdf
The AP style guidel says:
When to use a comma:
To separate a nonrestrictive appositive from the rest of the sentence.
- Raymond Turner, a biologist, described the species.
When not to use a comma:
Before or after a one-word appositive.
- The GABAA receptor agonist muscimol did not influence the response of WDR neurons in normal or allodynic animals.
The appositive in the last example is "muscimol", which is restrictive as it identifies "The GABAA receptor".
This means that the Oxford style guide and the AP style guide give opposing prescriptions.
Another style guide I found here says:
If an appositive is non-restrictive—that is, if it doesn’t contain
essential information for identifying the noun that it follows—it is
off-set by commas. In the following example, the appositive a doctor
is helpful, but does not necessarily identify the preceding noun.
- My cousin, a doctor, is going to join the Peace Corps.
appositive is restrictive—that is, if it contains essential inform
ation for identifying the noun that it follows—it does not require
any added punctuation. In the following example, the appositive
David identifies the noun that it follows:
- My cousin David is
going to join the Peace Corps.
Note, the AP style guide seems to prohibit ", Steve," because it's a one-word appositive, not because it's restrictive or non-restrictive.
On the example of David Cameron as the appositive of prime minister, I assume it's taken that David Cameron is non-restrictive as there is only one prime minister. In the same way, I think "Steve" is a non-restrictive appositive because we take it that Jenny has one partner.
Given this information, and if we ignore the AP style guide which prohibits single word appositives from being "set off" by commas, then surrounding "Steve" with commas would probably be the best thing to do.