I had forgotten I posted this question, and now have similar hardware in hand and the answers above may not be correct. I wanted to post what I know in case anyone else is anticipating this issue.
We purchased the WS-C3560CX-12TC-S, which is only gigabit, and those appear as gigabit 0/15 and 0/16, continuing the numbering of the last regular port gi0/14. They are running
C3560CX Software (C3560CX-UNIVERSALK9-M), Version 15.2(6)E1
We also have access to one WS-C3560CX-12PD-S, which does tenGig, and it is running
Cisco IOS Software, C3560CX Software (C3560CX-UNIVERSALK9-M), Version 15.2(4)E4, RELEASE SOFTWARE (fc2)
On that one the ports are numbered as GigabitEthernet1/0/1 thrugh 16, then TenGigabitEthernet1/0/1 and 1/0/2. Because that one is not completely under our control I have not had opportunity to plug in a 1g SFP, but I find it interesting the numbers are different entirely with three segments not two, perhaps because of the separate ten gig section (though read on).
Finally we have 3650's (WS-C3650-24TD) running
Cisco IOS Software [Denali], Catalyst L3 Switch Software (CAT3K_CAA-UNIVERSALK9-M), Version 16.3.6, RELEASE SOFTWARE (fc3)
These I have experimented with, and their ports are numbered:
GigabitEthernet 1/0/1 thru 24
GigabitEthernet1/1/1 thru 1/1/2
TenGigabitEthernet1/1/3 thru 1/1/4
This one also restarts the numbering in the SFP section but numbers the gig and tengig section sequentially. When you plug in a 1G SFP into the latter ports, they remain TenGigabitEthernet1/1/3 or 1/1/4 and do not change names (nor numbers).
#show int te1/1/4 cap
Type: 1000BaseSX SFP
So while I cannot confirm the behavior with a 3560 (since I have not had opportunity to plug a 1g pim into a 10g capable slot), the 3650 definitely does not change names when that is done, and these are all running pretty similar IOS-XE versions.
So my GUESS is that the answer to the original question is that they do not change names or numbers. If I have opportunity to try that other 3560 I will update this.