From the Overview:

Succession of Clan Buchanan Chiefs

The first six Clan Chiefs are poorly represented in historical records and are included by some Clan historians and omitted by others. Buchanan of Auchmar and Guthrie Smith commence their respective numbering of Chiefs at a different person, and describe a different order and number of Chiefs following Sir Walter 11th of Buchanan. In part this is due to the heir apparent not succeeding to the chiefship before he dies and chiefship passing directly from grandfather to grandchild. The following lineage reconciles Guthrie Smith and Buchanan of Auchmar and their respective numbering is in parenthesis.

• 1st – [[Anselan O'Kyan, 1st Laird of Buchanan Anselan O'Kyan, 1st Laird of Buchanan] Anselan O'Kyan],[62][63] son of a petty king from Ulster, Ireland, in the service of Malcolm II of Scotland from whom he received a grant of land in Lennox. He married [[Unknown Heiress of Denniestoun Unknown Heiress of Denniestoun] an heiress of Denniestoun] and by her had a son, [[John Mc Causland de Buchanan, 2nd Laird of Buchanan John Mc Causland de Buchanan, 2nd Laird of Buchanan] John].
• 2nd – [[John Mc Causland de Buchanan, 2nd Laird of Buchanan John Mc Causland de Buchanan, 2nd Laird of Buchanan] John],[64] whose son and successor was [[Anselan McCausland, 3rd Laird of Buchanan Anselan McCausland, 3rd Laird of Buchanan] Anselan].
• 3rd – [[Anselan McCausland, 3rd Laird of Buchanan Anselan McCausland, 3rd Laird of Buchanan] Anselan],[65] whose son and successor was [[Walter, 4th Laird of Buchanan Walter, 4th Laird of Buchanan] Walter].
• 4th – [[Walter, 4th Laird of Buchanan Walter, 4th Laird of Buchanan] Walter],[65] whose son and successor was [[Gerald, 5th Laird of Buchanan Gerald, 5th Laird of Buchanan] Girald].
• 5th – [[Gerald, 5th Laird of Buchanan Gerald, 5th Laird of Buchanan] Girald also called Bernard],[65] whose son and successor was [[Mcbeath McCausland, 6th Laird of Buchanan Mcbeath McCausland, 6th Laird of Buchanan] McBeath].
• 6th – [[Mcbeath McCausland, 6th Laird of Buchanan Mcbeath McCausland, 6th Laird of Buchanan] McBeath (MacBethe/McBeth)] McCausland,[65] whose son and successor was [[Anselan McCausland, 7th Laird of Buchanan Anselan McCausland, 7th Laird of Buchanan] Anselan]. http://en.wikipedia.org/wiki/Clan_Buchanan

I've removed the (MacBethe/McBeth) from the Middle Name field - because that's patently unneccessary. I'll put it in the aka once we decide.

https://kirkbuchanan.com/history

Weave through the traditional mythical origins of the clan and you'll find a charter in 1225 of the island of Clairinch in the southeast corner of Loch Lomond. This was granted by the Earl of Lennox to Anselan, son of Macbeth McCausland (sometimes recorded as McCaslan; McCauland; or Cauland), for the payment of a pound of wax every Christmas. Anselan was already a knight – Sir Anselan of Buchanan, and held lands on the loch shore and the name means ‘House of the Canon.’ He descends from one of the leading families of the ancient Celtic Church.

5th – Girald also called Bernard,[66] whose son and successor was McBeath.

6th – McBeath (MacBethe/McBeth) McCausland,[66] whose son and successor was Anselan.

7th – Anselan McCausland,[67][66]https://en.wikipedia.org/wiki/Clan_Buchanan Notes are from:

• [66 Buchanan of Auchmar, William (1733). The Historical and Genealogical Essay Upon the Family and Surname of Buchanan. Glasgow: Gale ECCO. p. 19. ISBN 978-1170761922.
• [67] Guthrie Smith, John (1896). Strathendrick and its Inhabitants from Early Times (1st ed.). Glasgow: James Maclehose and Son. p. 283.

Taking my Dad to school boy rugby. Back later

So, if Mcbeath McCausland is actually the son of Girald, then this seems to be an odd instance of the use of Mc to mean 'descendant of' not 'son of' Anselan. Alternatively Girald is not his father, the 3rd Laird is.

As to how a surname becames a first name - the answer is that Macbeth isn't actually a surname, and even the 11th Century king Macbeth had it as his first name:

Macbeth's full name in Medieval Gaelic was Mac Bethad mac Findlaích. This is realised as MacBheatha mac Fhionnlaigh in Modern Gaelic, and anglicised as Macbeth MacFinlay (also spelled Findlay, Findley, or Finley). The name Mac Bethad, from which the anglicised "MacBeth" is derived, means "son of life".[10] Although it has the appearance of a Gaelic patronymic it does not have any meaning of filiation but instead carries an implication of "righteous man"[10] or "religious man".[11] An alternative proposed derivation is that it is a corruption of macc-bethad meaning "one of the elect".[10]https://en.wikipedia.org/wiki/Macbeth,_King_of_Scotland

:-)