Unfortunately the item in N & Q on Thomas Coulican Phœnix is disappointing. The author quotes the entry from Lady Shelburne's diary as an instance in which Phœnix is used for a person's last name. Here's the item in full.
Phœnix. -- Some time ago there was a correspondence in "N. & Q." as to the origin of the family name Phœnix. The following quotation, from Lady Shelburne's diary may therefore perhaps be of interest to some of your readers: --
"November 25 . -- This morning I had christened at St. George's Church, a little negro boy of five years old, that was given me by Mr. Richard Wells on Friday last, by the names of Thomas Coulican Phœnix; the latter he had been called after the ship he was brought in. He is pretty, and very good humoured, and I hope by proper care will turn out well." -- Life of William, Earl of Shelburne, by Lord Edmond Fitzmaurice, ii. 181.
A. O. V. P.
Source: Notes and Queries, 5th Series, Vol VII, p.186 (Mar 10, 1877).
Addendum: Notes and Queries had many contributors like A. O. V. P. who took an interest in the origins of names. The index has lots of entries for unusual names of people and places. There's also a lot of interest in the origins of words, and phrases, songs, obscure expressions, and the like. I think N & Q attracted much the same folks as those who keep Wikipedia going strong.
Another of A. O. V. P.'s short pieces is on the phrase "on tick" meaning obtained on credit rather than paid for in cash. He writes:
"On tick." -- It is commonly thought that the phrase to buy "on tick" is modern slang. It occurs, however, in the year 1696 in the Diary of Abraham de la Pryme, published by the surtees Society: -- "Here is very little or no new monney comes yet down amonst us, so that we scarce know how to subsist. Every one runs upon tick and those that had no credit a year ago has credit enough now." -- p.100.A.O.V.P.
Source: Notes and Queries, 5th Series, Vol. VII, p. 46 (Jan 20, 1877).
Wikipedia on Abraham de la Pryme
Find the Diary of Abraham de la Pryme in a library (not where I work!)
On the shortage of silver coin in 1696 see: MINTS and the recoinage of 1696
Old coins, the ones that Abraham de la Pryme found to be scarce.
New coins, minted in the reign of William and Mary at roughly the time de la Pryme was writing his complaint. (It took time for the new coins to penetrate to his locale.)